𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, January 14, 2023
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Gemini index for the day: gemini://gemini.techrights.org/2023/01/14/


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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ Edda Franz, EPO’s Principal Director General Administration, Leaves EPO Amid Growing Chaos and Orchestrated Efforts to Divide the EPO’s Staff | Techrights

⦿ User Input ’Forms’  -  Akin to Webforms  -  in Gemini Protocol Using CGI (a Chess Game Example) | Techrights

⦿ IRC Proceedings: Friday, January 13, 2023 | Techrights

⦿ [Meme] How EPO Presents the Male-Dominated EPO | Techrights

⦿ Microsoft Rumour Mill About January (and July) Waves of Layoffs | Techrights

⦿ [Meme] Sirius Almost Half a Million Behind (2 Years Ago)  | Techrights

⦿ When the Employer Asks for Help or Personal Favours Outside Work (and Staff Cannot Politely Decline Because of the Salary) | Techrights

⦿ Sirius in the Era of ’Husband and Wife’ (or CEO and Director) | Techrights

⦿ [Meme] Fully Allowed to Speak About Injustice | Techrights

⦿ New Word/Term for Microsoft Layoffs: Unlimited Time Off | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2023/01/14/edda-franz-leaves/#comments
		http://techrights.org/2023/01/14/gemini-protocol-input/#comments
		http://techrights.org/2023/01/14/irc-log-130123/#comments
		http://techrights.org/2023/01/14/male-dominated-epo/#comments
		http://techrights.org/2023/01/14/microsoft-waves-of-layoffs/#comments
		http://techrights.org/2023/01/14/sirius-business-balance/#comments
		http://techrights.org/2023/01/14/sirius-family-butler/#comments
		http://techrights.org/2023/01/14/sirius-in-the-couple-era/#comments
		http://techrights.org/2023/01/14/speak-about-injustice/#comments
		http://techrights.org/2023/01/14/unlimited-time-off/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2023/01/14/dortmund-free-software/#comments
		http://techrights.org/2023/01/14/kde-frameworks-5-102-0/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 75

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/edda-franz-leaves/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/edda-franz-leaves/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Edda_Franz,_EPO’s_Principal_Director_General_Administration,_Leaves_EPO_Amid
Growing_Chaos_and_Orchestrated_Efforts_to_Divide_the_EPO’s_Staff⠀✐


Posted in Europe, Law, Patents at 3:06 am by Dr. Roy Schestowitz


Video_download_link | md5sum 7cb2e512f130af86f7f2395fc168904c
EPO Separating the Examiners
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-union-busting-hallmark.webm


Summary: Europe’s second-largest institution is resorting to tactics one might
expect to find in a factory floor or sweatshop in Communist China; workers are
being separated from their work friends, whom they lose contact with (might not
even be sure if they left the Office), in what’s likely an effort at union-
busting (Taiwan exercises several more union-busting tactics). There’s
considerable doubt about the legality of this in Germany and The Netherlands.
“In the middle of December,” we now learn, “Ms Edda Franz, PD General
Administration who was in charge of the project, left the Office unexpectedly.”


“ENOUGH IS ENOUGH!” THE EPO continues to crush its very own staff. Benoît
Battistelli and António_Campinos could never tolerate dissent, so they try to
“divide and rule” the staff, quite likely in violation of domestic laws (they’d
claim to be immune to these as international organisations) and in violation of
international labour laws (they like to simply disregard rulings against them,
even if ILOAT decisions are fully enforceable and binding, unless or until ILO
cans EPO… maybe vice versa, but then goes out the window one common excuse for
the EPO’s immunity).


The media’s unwillingness to cover these scandals is proving harmful to many
workers. Consider some of the_new_comments in this thread; the German
government is very much complicit at this point, including the ministry of
‘justice’ and the FCC.


The latest publication from the Central Staff Committee (CSC) of the EPO
focuses on a subject it discussed_half_a_year_ago when we argued “EPO
Management Behaves As If the Goal is to Shut Down and Outsource the Patent
Office”.


As it turns out, Edda Franz abruptly left and what’s left of examiners will
suffer profoundly from a torturous regime whose priority seems to be…
inconveniencing and threatening_staff.


“Since the last Working Group meeting of 21 November 2022,” the CSC wrote,
“management has unilaterally made radical changes to the project “Bringing
Teams Together”. According to information now provided to line managers, the 3-
day rule will not guarantee an allocated fixed workplace anymore. Line managers
are asked to proceed on the basis of quotas (70% of workplaces) which will
trigger divisive discussions among team members.”


Here’s the full publication:


     Munich, 12 January 2023
     sc23002cp


     § Bringing Teams Together:⠀➾


     § The divisive exercise⠀➾


     Since the last Working Group meeting of 21 November 2022, management
     has unilaterally made radical changes to the project “Bringing Teams
     Together”. According to information now provided to line managers,
     the 3-day rule will not guarantee an allocated fixed workplace
     anymore. Line managers are asked to proceed on the basis of quotas
     (70% of workplaces) which will trigger divisive discussions among
     team members. This paper gives more details of what we learnt about
     the revised plans of the administration.


     Dear Colleagues,


     From survey…
     Back in September 2022, the administration asked line managers to
     make surveys among their teams. Colleagues were asked how often they
     intend to come to the Office premises, whether they have specific
     conditions justifying an allocated fixed workplace and whether they
     would accept a workplace-for-the day. The message cascaded down at
     the time was that the 3-day rule for getting an allocated fixed
     workplace1 was that everybody would get what they want. Ms Simon
     (VP4) had already assured in a meeting with the Local Staff Committee
     Munich that a whole team wishing to come to the office premises 4 or
     5 days per week on a regular basis would be “perfectly” accommodated
     with allocated fixed offices for each team member.


     In the Communiqué of 14 September 2022, the administration announced
     that they were “currently still gathering detailed information on the
     needs of all DG1 staff concerned from their line managers”. The lack
     of popularity of the project also triggered the administration to
     postpone the moves in The Hague and Pschorrhöfe buildings until the
     beginning of 2023.


     …to broken promises…
     On 17 November 2022, the Office announced the revival of the project
     and that “all teams will now work together with their managers in The
     Hague and in the Pschorrhöfe buildings to finalise a detailed
     accommodation plan by January 2023”. Line managers were still
     expecting that they could prepare a plan matching what their
     colleagues expressed in the surveys.
     _____
     1 The term workplace is the one used by the administration in the
     GCC/DOC 13/2022 and designates a workstation comprising
     a desk, a chair and IT equipment. A workplace can be in an individual
     office room or in a shared office room with other
     workplaces.


     =====================================================================
     Management invited staff representation to a Working Group meeting on
     21 November 2022. In the meeting, the administration revealed
     worrying changes to their approach. Line managers will be tasked to
     check the history of presence of staff in the premises. At the time,
     the administration said that the 3-day rule for being eligible to an
     allocated fixed workplace would cease to be a simple guideline and
     would become a strict criterion.


     …and arbitrary action
     In the middle of December, Ms Edda Franz, PD General Administration
     who was in charge of the project, left the Office unexpectedly. The
     project is now in the hands of Ms Simon (VP4) assisted by Ms Bergot
     and Mr Brunelle (as deputy site managers for Munich and The Hague
     respectively).


     At the same time, line managers started to cascade down radical
     changes to the project to
     their teams:


     − For each Directorate, a specific number of workplaces (70% compared
     to present) will be allocated in the buildings.


     − The 70% workplaces will be split into assigned fixed workplaces and
     workplaces-for-the-day. In some directorates, a maximum of 50% of the
     allocated workplaces would be assigned fixed workplaces. Consequently
     only 35% of staff of that directorate will have an assigned fixed
     workplace. In other directorates, the share of assigned fixed
     workplaces was communicated to range between 50% and 70% of the quota
     allocated to the directorate.


     − Team Managers with many staff coming often to the premises will
     have to try to get allocated fixed workplaces from other teams with
     more regular teleworkers.


     − The allocation of a fixed workplace will be subject to regular
     reviews (e.g. every six months).


     Such features of the project were never discussed with the staff
     representation. The administration has now moved from an allegedly
     flexible system to an arbitrary quota-based system.


     The divisive exercise
     The reaction of staff is very negative. The whole survey exercise
     made in September 2022 turns out to be useless. Line managers are now
     in the difficult position of allocating workplaces to their team
     members on the basis of a quota not taking into account the wishes of
     their team.


     We now hear the following:
     • Some line managers now say that coming five days a week to the
     Office premises cannot guarantee an allocated fixed workplace
     anymore. This contradicts the statement made by Ms Simon (VP4) in the
     December meeting of the Administrative Council that “anyone coming at
     least three days per week will have an allocated fixed workplace”.
     • Some line managers confess that allocating only workplaces-for-the-
     day to everyone would be easier (!) and some even dare say they will
     do so.
     • Some line managers plan to split the week among colleagues in order
     to optimise the


     =====================================================================
     use of workplaces-for-the-day. Such a proposal would go against the
     principle of flexibility of teleworking and would lack support as
     Mondays and Fridays are currently the preferred choice for
     teleworking.


     • Some line managers say that staff members accepting a shared office
     (namely several workplaces in the same room) would increase their
     chances of having an allocated fixed workplace. This would go against
     the principle of individual workplace allocation promised by Mr
     Campinos.


     Instead of “bringing teams together”, the project will divide teams
     and cause conflicts.


     Conclusion


     Back in June 2022, the staff representation had published a paper
     estimating the percentage of workplaces-for-the-day necessary to
     empty some EPO buildings. At the time, management had tried to
     prevent the publication of the paper by alleging that it contained
     wrong information without saying which. The figures published at the
     time were actually very close to the ones circulated by line managers
     now.


     Mr Campinos acknowledged his ambition to rent out EPO buildings in
     the GCC meeting of 5 July 2022 and the Communiqué of 13 July 2022. Mr
     Campinos promised that “any potential rental revenues would be paid
     into the RFPSS”. However, this is of no direct help for the active
     staff.


     While the staff representation sees the necessity of a reasonable use
     of resources and energy, e.g. avoiding to heat unused office space,
     there must be a better solution than simply kicking people out of
     their workplaces. After all, our homes are not occupied 100% of the
     time and, yet, we do not leave our homes. We just turn the heating
     down and manage to find solutions tailored to our individual needs.
     We should expect that our employer also takes responsibility.


     The present problems associated with emptying several buildings
     simultaneously was created by management itself. Once again, upper
     management chose an arbitrary solution without considering the
     repercussions at team level and ignoring the feedback given by the
     staff representation. The project as currently foreseen will cause
     significant disruption in the work of staff. Further, transforming
     the personalised workplaces as they are now into standardised,
     impersonal, unlocked offices, where each office is exactly the same,
     seems to us the worst idea since the installation of glass walls. It
     is now up to line managers and their teams to pay the price of poor
     management.


     The Central Staff Committee


An office wanting to actually attract talented staff would not intentionally
choose a policy that staff patently hates. █


The EPO needs to update its_site already. Edda Franz left last year, but this
is what it presents today:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Edda_Franz,_EPO⦈_


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⣿⣿⣿⣿⣿⡇⠀⠀⣿⢀⢸⣿⣶⣿⣧⣀⠰⣮⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡌⠙⠙⠋⠃⣣⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣿⠟⢛⡖⠂⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⣿⠈⣼⣛⠛⢡⣌⣄⠀⢹⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢷⣶⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠿⢷⣶⣶⡄⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⡇⠀⠀⣿⠀⣿⣟⣄⢿⣷⠀⠀⠘⢿⠌⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣠⠂⠀⣦⣄⣠⡤⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣰⡄⠀⡉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⡇⠀⠀⣿⠀⣿⣿⣧⣠⣄⢀⣀⠄⠀⡀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⢿⣿⣿⡏⠀⠀⠀⢳⣀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣾⣧⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿
⣿⣿⣿⣯⣀⡀⠀⠀⣈⠀⠁⡹⠸⣿⡏⠁⠀⢠⡞⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠿⠍⢴⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠿⣿⣏⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣛⠇⠀⠀⠀⠀⢰⡷⠀⢹⣷⣖⣴⣿⡙⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣦⣄⣞⠛⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣄⡀⠀⡄⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣽⣤⢈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣷⡤⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣛⡁⠁⢁⣴⣿⡀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣸⣿
⣿⣿⣿⣿⠻⠛⠛⠛⠛⠛⢿⡻⠻⠛⠛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠻⠻⠛⠛⡟⠻⠛⣛⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠛⠛⢻⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⡿⢿⢿⠿⠿⠿⡿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⣿⢿⡿⠿⠷⡿⠿⠿⠿⡿⢿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⣿⢿⠿⠿⡿⠿⠿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣷⣿⣾⣾⣾⣶⣶⣿⣷⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣾⣿⣷⣶⣶⣷⣶⣷⣶⣶⣿⣷⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣷⣷⣷⣷⣶⣿⣷⣷⣿⣶⣶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 376

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/gemini-protocol-input/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/gemini-protocol-input/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ User_Input_‘Forms’_—_Akin_to_Webforms_—_in_Gemini_Protocol_Using_CGI_(a_Chess
Game_Example)⠀✐


Posted in Protocol at 2:37 am by Dr. Roy Schestowitz


Video_download_link | md5sum aa60abd1c99a642e58019f6591366321
Gemini and Chess
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/gemini-user-input-chess.webm


Summary: Gemini Protocol is a lot more versatile than people are led to
believe; with complexity passed to the server side, there are already some
board games and riddles available in Geminispace


THE Gemini Protocol is very, very simple. But it does facilitate user input, so
some people have taken advantage of this to create stuff that’s akin to Webform
(in the World Wide Web). Abrasive types like to moan about if not troll Gemini
for its simplicity, but simplicity itself can be immensely powerful (like
chaining of UNIX programs).


“It didn’t work as expected, but then again, this chess implementation (and/or
the server) was recently overhauled.”In the video above I’ve attempted to
demonstrate how people can play chess with friends over Gemini Protocol. It
didn’t work as expected, but then again, this chess implementation (and/or the
server) was recently overhauled. █



                    ䷩ 𝚕𝚒𝚗𝚎 424

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/irc-log-130123/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/irc-log-130123/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_January_13,_2023⠀✐


Posted in IRC_Logs at 3:33 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-130123.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-130123.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-130123.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-130123.gmi
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmWJhYnaJPebiv8STXqAm9f2aaFAPao3cjyQS7pw3WuLJg #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmeX1uQ6ec6aA6Bph2dQ1SxPkZyBuCg1iftmknPVHxPspT (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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                                                 IRC log for
                                                 #boycottnovell-
 QmVre24t74HcJjZpgKmkMu7JitvpqyyyuXrH7LNdyn4wo2 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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                                                 IRC log for
                                                 #boycottnovell-
 QmbFebkAtkhgZ73PuEws2AMVe5ZXaf47LT6bYnciXcsr5m social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
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                                                 IRC log for
 QmeUMq4Ldh3p3VGbUSWyiBMKGwq4udcmwRSQfFXDF9FmbK #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmXERpi77f6vADZa49nmvg8DtxJozSiF7y25ZnX95Dtuzp (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
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                                                 IRC log for
 Qmd7kdMh4UEax4uw1GAj16ym3731BCSQk9mbYLWeKC6pH3 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 Qmd57nS3dCzHFUnDJnw88w4oe5Efpvk7eHE1WZNKjq6CiV (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmbknBr8z72ETqFBT4rXhL1uPfXcKUcbpKNDsm6M8BcGQp



                    ䷩ 𝚕𝚒𝚗𝚎 551

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/male-dominated-epo/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/male-dominated-epo/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_How_EPO_Presents_the_Male-Dominated_EPO⠀✐


Posted in Deception, Europe at 3:29 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Hideous_Journal:_Our_web_site_has_many_women,_also_those_who
left_already;_managers_who_attack_staff⦈_


Summary: The sexist EPO (gender-balancing_for_PR's_sake while discriminating
against_female_colleagues) continues to paint a false and highly misleading
image of diversity; apparently some of the women in management won’t be used as
political props for much longer


⠉⠉⠉⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⣉⣉⣿⣿⣿⠿⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⣿
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿⠟⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠈⠈⠩⡏⠉⠉⠉⠉⣏⢙⢹⢛⠛⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⡿⠷⠾⡶⠷⠶⢷⠶⢶⢶⣴⣷⣴⣼⣼⣬⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣁⣀⣈⣇⣀⣀⡈⡀⡇⣾⠀⠀⠰⠀⠀⠀⠂⠁⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⣠⣶⣿⣿⣿⣗⣂⡤⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢙⠙⠛⢻⡛⠛⠻⠛⠟⠛⣻⣿⣷⣷⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⠿⠛⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⣿⣿⣿⡿⡿⠿⢿⣶⣤⣴⣤⣤⣼⣤⣤⣤⣤⣅⣄⣺⣿⣿⣿⣿⣿⣿⣿⡟⢁⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠙⢿⣿⣇⣀⢰⠀⡁⢸⠀⠀⠆⡆⣼⠁⠇⡇⢸⢉⠉⡏⢩⢉⣿⣿⠟⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣻⣿⠄⠀⠀⠐⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣏⣽⡿⢫⣾⣿⣷⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⣶⠾⠚⢉⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣛⣛⠋⠁⠈⣿⣿⠃⣼⣿⣿⡿⠛⢉⣈⣉⣉⠛⠛⠛⠛⠛⠛⠋⠉⣉⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⣤⣀
⠀⠀⠀⠀⠀⢠⣾⣿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⣶⣿⠃⣸⠿⠋⣡⣴⣾⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣦⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣰⣿⣿⣿⣷⡄⢹⣿⣿⣿⣿⣿⣿⣿⡎⠉⠉⠉
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣠⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣭⣭⠍⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠝⢻⣿⣿⡝⢫⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣯⠭⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠁⠀⠀⠈⣼⢟⣯⣽⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⠇⡄⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣷⣶⠀⢹⣿⣿⣿⣿⣿⣿⣿⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⢿⣿⣿⣿⣱⣶⣶⣦⡀⠀⠀⠀⢸⣷⣿⡿⣛⣉⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣛⣟⣿⣿⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⣿⣻⣿⣻⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣶⣾⣿⣿⠿⣛⣻⣿⣿⣾⣿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⢨⣟⣿⣿⣻⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣛⣯⣵⣾⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣧⣦⣼⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⢸⣿⣿⣿⣷⡇⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣷⢲⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡇⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿
⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠓⠙⢛⣉⣉⣓⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡞⣿
⣿⣿⣿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣡⣴⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣉⣉⣉⣉⣉⣀⣘⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣄⣀⣀⣸⣿⣿⣿⣿⣿⣇⣽
⣿⣿⣿⣷⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣀⣀⡀⠀⠀⠛⠛⠻⠿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣍⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⡿⠕⠚⠿⣿⡿⠋⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠋⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠛⢻⠛⢻⠛⢻⠛⡟⢻⠛⢻⡟⠛⢻⠛⢻⠛⠛⡟⠛⢻⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣛⣛⣛⣻⣿⡿⢿⣿⣿⣿⡿⡟⠻⣩⣽⣿⣿⣶⣶⣿⣿⣿⣭⣽⣿⣛⣛⣛⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠘⠠⠘⠀⠀⠸⠠⠀⠀⠐⢺⠀⣹⠀⠀⡧⢌⠹⣿⣿⣿⣿⣿⣷⡄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣧⣧⣤⣼⣤⣤⣧⣤⣴⣤⣧⣤⣼⣤⣼⣤⣦⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⢹⠉⠉⠙⢩⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⢸⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⠀⢿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠿⠿⠿⡿⠿⣿⠿⢿⡿⢿⠿⣿⠷⢿⡿⠿⢿⠿⢿⠿⠿⠿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⡄⠈⢿⣿⣿⣿⣿⡇⠀⢳⠀⢰⡆⢰⡇⡀⠋⢰⣀⡇⠀⢸⣿⡀⠠⣶⠀⡞⢀⢸⠀⠲⠀⢲⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⠆⡀⠻⣿⣿⣿⣀⣄⣸⣀⣸⣇⣸⣀⣄⣠⣘⣀⣇⣀⣘⣿⣀⣀⣿⣀⣇⣠⣀⣀⣿⣀⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⠿⣟⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣴⣿⣿⣦⡀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢠⣶⣿⣿⣷⣯⣫⣾⣿⣿⣿⣷⣕⣻⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠃⠀⠀⣿⣿⣛⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣈⣉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⣀⠀⡈⠙⠿⣿⣿⣿⣧⠀⢄⣀⠻⣿⣿⡿⣿⣿⣹⣿⣭⣽⣿⡿⣻⣿⣿⣿⣦⡀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣷⣦⣀⠙⠻⢿⣆⠀⢏⣼⣾⣯⣝⣿⣿⣿⣷⣿⣻⣷⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡽⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠉⠂⠘⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣼⣿⣿⣿⡿⠀⠀⠀⠀⢀⣤⢀⣤⣄⠀⣿⣿⡟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⠸⣿⣿⣿⣿⣷⡀⠀⢀⣀⢸⣿⡿⣫⣭⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣾⣿⣿⣶⣭⡛⢿⣿⣿⡿⣿⣿⣷⣽⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡷⣨⣾⣽⣫⢞⣛⡏⢉⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣧⡭⣰⣾⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⠏⠀⠉⠉⣨⣭⡶⠰⠟⠃⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣮⡙⠢⢐⢡⡔⣀⠤⠶⠶⠏⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣲⣦⣳⣽⣧⢒⣒⣂⠉⢉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡼⣛⣾⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣹⡽⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣮⡅⡉⠉⠉⣼⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 625

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


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✐ Microsoft_Rumour_Mill_About_January_(and_July)_Waves_of_Layoffs⠀✐


Posted in Microsoft, Rumour at 10:41 am by Dr. Roy Schestowitz


The word coming through the grapevine (I spoke to people) is that layoffs are
imminent, spending cuts are already deep, and the situation is grossly under-
reported (media_dysfunctional)


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇MSFT_messed_up_headcount_and_budgeting_badly._You_dont
increase_merit_budgets_right_before_recession._You_dont_go_ahead_and_hire_20K+
folks_in_the_year_recession_starts._July_will_be_much_worse,_much_much_worse.⦈_


Summary: A couple of new comments today suggest that not only are Microsoft
layoffs coming (rumour says next week and some can “confirm”) but there’s a lot
more on the way


⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠆⡟⣛⠛⠛⣟⢙⣿⡟⢍⢩⢫⡶⣘⢻⢛⢛⡛⠟⠛⡿⠹⢯⢸⠸⢛⡆⠖⣴⡸⣇⣶⠰⢸⡆⠆⣩⢸⡆⣿⡆⣿⡗⣟⢛⢻⣿⡛⣛⠛⠛⡛⡛⢷⢘⢻⢛⣿⢙⡻⣛⠻⣿⣬⣸⡆⣟⡛⡟⣛⢻⣿⡅⣷⡖⣦⣼
⣬⣿⣧⣩⣬⣄⣼⣨⣿⣧⣈⣈⣮⣬⣽⣦⣾⣌⣩⣬⣩⣿⣾⣯⣼⣤⣬⣧⣭⣽⣧⣼⣯⣴⣬⣥⣧⣽⣬⣧⣉⣵⣿⣧⣭⣼⣬⣿⣥⣿⣌⣩⡇⣫⣮⡼⢆⣾⣿⣎⣥⣝⣵⣿⣿⣯⣱⣅⣤⣧⣽⣼⣿⣥⣽⣸⣿⣿
⠿⢿⠿⣿⡿⠿⡿⢿⡿⠿⡿⠏⡟⣿⠿⢿⡿⠿⢿⣟⢻⣿⢛⡟⣿⠿⣿⠿⢿⠿⣿⡿⢿⡿⢿⠟⠝⠻⣿⡿⣛⡛⣿⠿⣿⠿⠿⡿⣿⣿⣿⣹⡶⢿⠿⡿⢾⠿⣿⠫⠛⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⣆⠬⢼⠘⢸⠊⠅⡇⣶⠰⠇⠇⠿⢸⠸⠄⠃⣿⡿⢧⢣⠇⡇⢇⠾⠾⢸⡆⠿⢸⠬⢸⠸⢆⡇⣿⠸⣿⣇⠿⠿⡅⠷⡸⢸⡆⠾⢸⢿⣿⠿⠃⠅⣧⢃⡇⠿⢸⠸⡇⡗⠍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⢹⡏⠉⢉⣉⠉⠉⣿⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣋⣹⠀⢸⡇⠀⠰⣾⠇⠀⢸⡇⠀⣉⣉⠆⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢠⠲⡤⠀⢸⡇⠀⡇⢩⠃⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⠀⢸⡇⠀⢈⣋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠛⠛⠛⠛⠛⠛⡟⢛⡏⠙⠛⠛⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠒⠀⠀⠀⢸⣿
⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠋⢀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⣛⣻
⣿⢻⠻⢻⠛⣛⡿⠿⡿⠿⠿⡿⡿⣿⠿⠿⣟⢿⠿⢿⠟⠿⠿⢿⠿⠿⢿⠿⠿⠟⡟⠏⠀⠜⠿⠿⠿⠻⠿⢿⠻⡿⡿⠛⠿⣿⠛⠿⢿⣿⠟⠿⠿⠿⡟⠿⡿⠿⠿⠿⠿⠿⡿⠿⡿⠿⠻⢿⣿⣿⣿⣿⣿⡇⡇⠦⢨⣿
⣿⣤⣥⣴⣼⣭⣧⣽⣤⣦⣦⣦⣮⣽⣤⣨⣯⣧⣴⣬⣤⣬⣮⣮⣥⣤⣿⣬⣧⡄⠁⣰⣥⣥⣀⣦⣯⣤⣄⣸⣬⣦⣬⣤⣲⣽⣯⣬⣮⣿⣥⣤⣬⣯⣧⣬⣮⣿⣤⣤⣤⣤⣧⣽⣦⣯⣼⣽⣿⣿⣿⣿⣿⣧⣭⣭⣭⣽
⣿⣈⣉⣙⡋⢈⣁⣉⣏⣅⠉⣪⣋⣇⣉⣉⣎⣉⣍⣹⣉⣉⣋⣉⣉⣁⣉⡩⠋⢀⣈⣉⣹⣏⣈⣉⣩⣹⠉⣉⣏⣑⣍⣉⣙⣁⣏⣉⣉⣛⣇⣁⣩⣉⣗⣀⣒⣔⣭⣇⣘⣓⣉⣹⣏⣉⣇⣪⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⠻⢛⡟⠟⢟⠟⠟⠟⠻⡻⡻⡟⣟⠛⢛⠻⢻⣿⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢼⣶⣶⣾⣷⡶⠶⡶⣶⣶⣶⣶⣶⣷⢶⣶⣾⣶⣶⣿⣿⣿⣿⡿⠁⣠⢾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣠⣛⡂⣾⣀⣆⣀⣇⣪⣸⣲⣂⣀⣐⣰⣳⣉⣖⣄⣆⣅⣿⠂⢀⣀⣐⣐⣿⣂⣀⣨⣚⣞⣇⣴⣂⣰⣨⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠩⢹⠉⠉⠉⠉⠋⠉⢙⠉⢉⠋⠉⠙⡉⠉⠙⠉⠉⠃⢀⢠⠉⠉⠫⠉⠉⠉⠋⣙⠙⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠠⠄⠀⡠⣤⠀⠀⠤⠤⠤⠄⡄⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⠋⣿
⣿⣾⣶⣶⣶⣶⣿⣷⣶⣾⣶⣾⣶⣶⣶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿

                    ䷩ 𝚕𝚒𝚗𝚎 689

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/sirius-business-balance/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/sirius-business-balance/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Sirius_Almost_Half_a_Million_Behind_(2_Years_Ago)⠀✐


Posted in Finance, Free/Libre_Software at 3:43 am by Dr. Roy Schestowitz


It has gotten worse since


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sirius_business_balance⦈_


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Doctor_Harold:_Oh,_I_see..._Sirius_is_f***ed⦈_


Summary: Sirius_‘Open_Source’ is in a bad state


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣾⣿⣥⣼⣿⣿⣿⣿⣤⣧⣤⣤⣤⣷⣿⣧⣿⣴⣼⣴⣼⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣮⣬⣽⣷⣿⣽⣿⣥⣿⣽⣿⣧⣿⣬⣥⣽⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⢿⢿⡿⢿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⡿⠿⠿⠿⣿⠿⠿⢿⠿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠿⠿⣿⠿⠿⠿⠿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⡄⠀⢸⠀⠀⢸⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⡄⠀⠘⠀⠀⢀⣀⡇⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⡇⠀⢸⠀⠀⠈⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⡀⠀⠀⠐⢾⠀⠀⠈⠉⡇⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⡇⠀⢸⠀⠀⢰⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⠉⠁⡄⠀⠀⠀⠀⢰⣶⡇⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣀⠀⠀⢀⣼⡀⠀⢸⠀⠀⡀⠀⣿⣿⡇⠀⢸⣿⣿⣄⠀⠀⠀⣠⡀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡀⠀⡀⠀⣿⣿⡟⢁⣴⣦⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣇⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⡍⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡠⡆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠚⡠⠁⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣱⡷⠀⠀⠀⠀⠀⠀⠀⣠⣷⣷⠀⡇⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⢨⣧⣿⣿⣧⡝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⠇⠆⠀⠀⠀⠀⠀⣴⢻⠋⢀⡀⠀⠃⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⣿⣿⠸⠀⠀⠀⠀⠀⣸⢫⠆⢀⣿⣿⡁⢸⣿⢻⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣼⣿⡇⠀⠀⠀⠀⢀⣴⡿⢠⡇⣼⣏⢀⠀⣽⡉⢘⣿⡷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⠁⠀⠀⠀⢰⡿⢱⣿⡇⣿⣿⠈⠀⣿⡗⠘⣻⠁⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⢃⣿⡟⡇⢸⡿⠀⠀⢸⡇⢰⡏⠀⠀⢠⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡜⣸⣿⡗⣛⣈⠁⠀⠀⠈⡇⢸⠀⢀⠶⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠿⠿⠿⢿⠁⠀⠀⠀⠀⢀⢡⣿⣿⡇⣿⣿⣦⠀⠀⠀⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡿⠿⠇⢻⣇⠀⠀⠀⠀⣀⢠⣤⡴⣿⡿⠛⠓⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢛⠛⠝⢿⡈⣿⠀⠙⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠈⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠉⠉⠉⢻⡟⠉⢻⠋⠙⠉⢙⠁⢸⡟⠉⢻⡿⠉⢻⡟⠉⠉⠉⢻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⡀⠉⠑⠺⡇⠀⢸⠀⠀⣶⣿⠀⢸⡇⠀⢸⡇⠀⢸⣄⡀⠉⠁⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡅⠈⠙⠀⢀⡇⠀⣸⡀⠀⣿⣿⠀⢸⣇⠀⠈⠁⠀⢸⡅⠈⠙⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣿⣿⣟⢉⡟⠛⡿⠛⠛⢿⣿⠛⠛⠚⠟⠿⠟⠿⠟⠶⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⠀⠰⠤⠃⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡅⠀⠠⢬⣿⠀⠀⠒⣤⣼⣤⣼⣤⡄⠀⠐⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠢⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡏⠀⠀⠈⣿⠀⠀⣶⣿⣿⣿⣿⣿⡇⠀⠰⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣷⣤⣤⣾⣿⣦⣤⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠃⠀⠀⡀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣤⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⣾⣿⡏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⡀⡆⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⣬⡇⠀⣹⡄⣷⢠⡄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡎⠀⣶⣿⣿⣟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⠀⠀⠹⡇⣿⣸⢱⡆⠀⣀⠀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡾⠀⣼⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠐⠆⠀⢸⡏⢸⡇⢰⣿⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣞⠃⢀⣿⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣶⠀⠀⠀⠀⢸⡆⠀⠘⡇⢸⣇⣿⠟⠀⠀⠀⠘⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 785

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/sirius-family-butler/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/sirius-family-butler/

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Gemini_version_available_♊︎


✐ When_the_Employer_Asks_for_Help_or_Personal_Favours_Outside_Work_(and_Staff
Cannot_Politely_Decline_Because_of_the_Salary)⠀✐


Posted in Free/Libre_Software at 8:49 pm by Dr. Roy Schestowitz


There were times I literally stayed at their home because they didn’t want to
spend money on suitable accommodation (e.g. hotel)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Sirius_CEO_-_obscured⦈_


Summary: At Sirius_‘Open_Source’ I was sometimes asked by management to look
after personal affairs or help family friends; employers aren’t supposed to
leverage their workforce like that


TECHRIGHTS deals with a variety of “Tech” issues and a broad range of “Rights”,
including so-called ‘IP’ so-called ‘rights’. There is currently a
constitutional crisis brewing in Germany and it_relates_to_patents, but today
we focus on labour rights pertaining to workforce outside the workplace.


“Some bosses exploit that, knowing it’s construed as impolite to say “no” to
the people who pay the salary.”As readers are aware, my wife and I resigned
last month and left our job (after a combined period of 21 years in that
employer). Today I’d like to highlight a likely common situation where the
employer tries to get workers to do personal favours outside the business or
outside the workplace. Many people don’t like to talk about it, as it might
come across as “moaning” or a lack of generosity. After all, some colleagues —
typically below the pay grade of their bosses — end up picking up post or
picking up the kids from school. They may end up like family assistants. They
try to “get ahead” by improving the relationship with the boss or, to put it
more bluntly, “sucking up” to the boss. It’s unprofessional, but it is still
done a lot. Some bosses exploit that, knowing it’s construed as impolite to say
“no” to the people who pay the salary.


In practice, bosses should never do this. It’s not like asking for sexual
favours, but it’s still bad. It’s better not to even ask or bother with such a
request.


Today’s example is old but still relevant. I can finally speak about it. The
CEO and his wife asked me to look into a site of a family friend from Spain, in
spite of language barriers and the site having nothing whatsoever to do with my
job. Like I’m a “home butler” of theirs, serving guests.


It started like this:


     Hi xxxxx,


     I have cced Roy into this mail as he knows a lot about wordpress so
     he should be able to help you sort out the problems you are having.
     I will leave you to chat between yourselves.


     See you in a few weeks 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


     xxxxxx xx


The person in question spoke, but with very weak English — to the point where
it’s extremely difficult to communicate at all. It was a massive language
barrier. I followed up:


     Hi xxxxx,


     Can you please show me your site and tell me what you are hoping to
     achieve, maybe with examples of sites that accomplish what you’re
     after?


     Regards,


The communication was informal, but I was expected to give technical help to a
family friend of the CEO and his wife. Here’s example of communication that I
received:


     Hi xxxxx!!


     Thanks!!! My mum thinks that she is going to pick me up hahaha so you
     will See her at the AirPort


     Hi Roy,


     Ill have to give you acces to the blog Cuz its not aviable now, Also
     Ive got allready a list with the things that I would like to change
     if its possible of course


     Do I give you access with this email?


     Thanks a lot for your help


     xxxxxxx
     Enviado desde mi iPhone


It didn’t go very far, but the point of the matter is, the manager was asking
me to provide support to someone who wasn’t a client but a personal friend.


On another occasion, more recently, the CEO was asking me to speak to a
personal friend who had become the target of a patent troll, as if I was some
unpaid ‘consultant’ on this matter.


“Next time I’ll phone you,” I said, “assuming you don’t keep an eye on E-mail.”
I spent a long time basically advising someone because he was a friend of the
CEO. Looking back (in retrospect), it was a waste of time as I was under no
obligation to do so. But because I was receiving salaries (for something
totally unrelated) I felt compelled to agree.


There should be very strict laws against this sort of thing. Paying someone a
salary for job X does not make one a “butler” for job Y. From what my wife has
told me, in some occupations and with some agencies there are official avenues
for reporting this. Apparently this sort of misuse or workforce became such a
big problem that confidential helplines/lifelines were thrown at workers,
offering resolution without retribution/reprisal from the employers
(threatening/blackmailing workers who report the practice/abuse). █


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣧⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠟⠿⠿⠟⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀
⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀
⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 986

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/sirius-in-the-couple-era/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/sirius-in-the-couple-era/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Sirius_in_the_Era_of_‘Husband_and_Wife’_(or_CEO_and_Director)⠀✐


Posted in Deception, Free/Libre_Software at 1:57 am by Dr. Roy Schestowitz


Video_download_link | md5sum e07915de3d9b82d54ea7b3b66fd312a9
A Sirius Relationship and Couple
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/mrs-sirius.webm


Summary: It’s hardly a scandal that a married couple was running the company
from around 2010 until almost 2018; but that may have been a poor role model,
as in later years one manager would bring in a spouse and two girlfriends into
the company in spite of unsuitable background; the video above ends the series
of articles about nepotism inside Sirius ‘Open Source’


THE company Sirius_‘Open_Source’ was owned and controlled by a husband and wife
when I joined almost 12 years ago. It still had plenty of geeks, including a
former Debian Developer. It had a large building, it had staff specialising in
different facets of operation (e.g. finance/accounting), and nepotism — if that
counts at all — was limited to the CEO. In all fairness, it’s quite common for
a couple to run a business. The only other example of nepotism (prior to me
joining) that I’m aware of is one colleague who joined because of his
boyfriend, who then became a colleague. He later left both him and the company,
but again, in all fairness his (ex)boyfriend was technical and a GNU/Linux
user. He looked after almost everything in the office, he was polite, and
generally amicable. It was devastating to the company when he left several
years ago. His certificates and his KDE desktop were still left there in the
office when I last visited (even a year after he had left).


“In all fairness, it’s quite common for a couple to run a business.”Looking
back at the whole thing (21 years in combined duration for my wife and I), the
CEO’s wife did a much better job than anything that came later and it seems
safe to attribute the collapse of the company to the deterioration of that
marriage (the CEO’s second marriage, ending around 2018 or 2019). It didn’t
take long for him to sell out to Bill_Gates (2019) and only weeks later the new
manager was bullying both myself and my wife. They were never held accountable
for it; not even an apology was offered.


The video above tells stories almost a decade old, corresponding to the_text
published_last_night. █



                    ䷩ 𝚕𝚒𝚗𝚎 1050

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/01/14/speak-about-injustice/#comments
    Gemini version at gemini://gemini.techrights.org/2023/01/14/speak-about-injustice/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Fully_Allowed_to_Speak_About_Injustice⠀✐


Posted in Law at 9:09 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Roy_is_talking_about_the_company⦈_


Summary: Sirius_‘Open_Source’ management does not share the ‘view’ (basic
right, not up for debate) that former staff can speak about the former employer
out in the open


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢆⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣼⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣿⣼⣿⣿⣿⡗⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣷⡭⢛⣛⣻⠿⢛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⢟⣤⢒⣛⣒⣼⣭⣷⣿⢸⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢫⣶⣿⣿⣯⣻⣋⣛⣣⣭⣭⠾⣛⣛⣛⡻⢿⣿⡜⣿⡿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣷⣎⢇⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣛⠿⣿⣿⣿⡿⢫⣾⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣜⠿⣿⣿⣿⡟⣽⣏⣾⣷⣼⣿⣷⠽⣟⣭⣾⣿⣯⣙⠿⣱⡇⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⡼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣶⣭⣭⣥⣛⣿⣿⣭⣽⣷⣾⣿⣿⡿⠿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣙⣙⣯⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢙⡛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣠⣤⣤⣤⣤⣤⣦⣤⣶⣶⣶⣶⣦⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠠⣤⣤⡄⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢆⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣼⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣿⣼⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣧⡭⢛⣛⣛⠿⢛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⢟⣤⢒⣛⣒⣼⣭⣷⣿⢸⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢫⣶⣿⣿⣯⣻⣋⣛⣣⣭⣭⠾⣛⣛⣛⡻⢿⣿⡜⣿⡿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⣎⢇⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣛⢿⣿⣿⣿⡿⢫⣾⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣜⠿⣿⣿⣿⡟⣽⣏⣾⣷⣼⣿⣷⠽⣟⣭⣾⣿⣯⡙⠿⣱⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣶⣭⣭⣥⣛⣿⣿⣭⣽⣷⣾⣿⣿⡿⢿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⠉⡉⢉⣙⣹⣯⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⠣⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢙⡛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣠⣤⣤⣤⣦⣴⣶⣶⣶⣶⣾⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠠⣤⣤⡄⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢦⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣼⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣯⣼⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣧⡭⢛⣛⠿⢿⣛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣢⢒⣛⣒⣼⡭⣷⣿⢸⣿⣿⣮⡙⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢫⣾⣿⣯⣻⣋⣛⣣⣭⣵⣿⣿⣿⣿⣿⣎⢿⣿⣿⡿⠿⠗⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣽⣿⣭⡛⢸⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⢸⣿⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⡜⣿⣿⣿⣿⣿⠿⢟⣃⡟⣭⣽⢻⣿⡿⣣⣿⣯⣛⠿⣱⡇⣤⣤⣦⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣮⣛⠿⣿⢸⣿⣼⣿⣷⣿⠿⣇⣭⡾⠿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣹⣯⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣶⣾⣿⣿⣷⣶⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⠣⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢝⡛⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⣦⣴⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣴⣴⣶⣶⣶⣶⣶⣾⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠠⣤⣤⡄⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢆⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣼⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣿⣼⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣧⡭⢛⣛⠿⢿⣛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣢⢒⣛⣒⣼⡭⣷⣿⢸⣿⣿⣮⡙⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢫⣾⣿⣯⣻⣋⣛⣣⣭⣵⣿⣿⣿⣿⣿⣎⢿⣿⣿⡿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣽⣿⣭⡛⢸⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⢸⣿⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣿⡜⣿⣿⣿⣿⣿⠿⢟⣃⡟⣭⣽⢻⣿⡿⣣⣿⣯⣙⠿⣱⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣮⣛⠿⣿⢸⣿⣼⣿⣷⣿⠿⣇⣭⡾⠿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣛⣩⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣶⣾⣿⣿⣷⣶⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢙⡛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣠⣤⣤⣴⣤⣴⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠠⣤⣤⡀⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢆⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣼⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣿⣼⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣧⡭⢛⣛⣛⠿⢛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢟⣤⢒⣛⣒⣼⣭⣷⣿⢸⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢫⣶⣿⣿⣯⣻⣋⣛⣣⣭⡭⠾⣛⣛⣛⡻⠿⣿⡜⣿⡿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⣿⣿⣌⢃⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣿⢿⣿⣿⣿⣿⢫⣾⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⣜⠿⣿⣿⣿⡟⣽⣍⣾⣿⣼⣿⣷⠽⣛⣭⣾⣿⣯⣛⠿⣱⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⡼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣶⣭⣭⣥⣟⣿⣯⣭⣽⣷⣾⣿⣿⡿⠿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣋⣛⣯⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢙⡛⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣴⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠠⣤⣤⡄⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢆⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣼⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣯⣼⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣧⡭⢛⣛⣻⠿⢛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢟⣤⢒⣛⣒⣼⣭⣷⣿⢸⣿⣿⣿⣷⣮⡻⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢫⣶⣿⣿⣯⣻⣋⣛⣣⣭⡭⠾⣛⣛⣛⡻⠿⣿⡜⣿⡿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣿⣿⣿⣿⣿⣿⣌⢇⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⡜⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⣿⢿⣿⣿⣿⡿⢫⣾⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣜⠿⣿⣿⣿⡟⣽⣍⣾⣿⣼⣿⣷⠽⣟⣭⣶⣿⣯⣛⠿⣱⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⡼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣶⣭⣭⣥⣿⣿⣯⣭⣽⣷⣾⣿⣿⡿⠿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣭⣫⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⠣⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢝⡛⣁⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣴⣶⣶⣶⣦⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠠⣤⣤⡄⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡶⢆⣀⣀⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⣬⣯⡻⣿⣏⣾⡿⢿⣿⣿⣷⡜⣿⣶⣄⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⡏⣿⣿⡇⣿⡸⣿⣿⣼⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡸⣿⣷⡿⠟⠙⢛⣧⡭⢛⣛⠿⣿⣛⣵⣿⣿⣿⣿⣷⡀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣠⢒⣛⣒⣼⡭⣷⣿⢸⣿⣿⣮⡙⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢫⣾⣿⣧⣻⣋⣛⣣⣭⣵⣿⣿⣿⣿⣿⣎⢿⣿⣿⡿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣭⣷⣭⡛⢸⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⢸⣿⣿⣀⡠⡉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⡜⣿⣿⣿⣿⣿⠿⢟⣃⡟⣭⣽⢻⣿⡿⣣⣿⣯⣛⠿⣱⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣮⣛⠿⣿⢸⣿⣼⣿⣷⣿⠿⣇⣭⡾⠿⣿⢿⣫⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣙⣻⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣶⣾⣿⣿⣷⣶⣿⣿⣿⠏⢾⣿⣎⢿⣿⣿⣿⢣⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠟⠋⠁⠀⠀⡘⣿⣿⣎⢝⡛⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣠⣶⣿⣿⡘⣿⣿⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⣿⣇⠹⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠘⣿⣿⣿⣿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠠⣤⣤⡄⠀⠀⢿⠟⠋⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠋⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⡽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠀⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣫⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⡿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣩⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣧⣦⡄⠉⣉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠟⣤⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⠀⠉⠉⠋⢰⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⣟⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢸⣿⣧⢲⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡋⠏⣸⡝⡝⠝⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡗⣀⣤⣀⠺⠿⢇⣴⣶⣶⣦⣶⣶⣶⣶⣿⣷⣿⣾⣷⣶⣭⣟⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠈⠉⠁⠉⠀⠈⠉⠉⠁⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠟⠾⠿⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣷⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⠖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⣿⣻⣯⣦⣚⢿⣷⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣶⣾⣿⡞⣿⢣⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡟⣸⣿⣿⢳⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣏⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣿⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢻⣿⣿⣛⢛⣸⣿⣯⣭⣭⡁⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⣿⣿⣷⡽⣿⡿⠿⣧⣛⣛⣿⣭⣷⣿⣿⣿⣿⠿⣿⡧⡠⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⠉⡉⢉⣋⣛⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡜⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⠋⠵⢾⣿⣿⣿⡿⠀⠀⠀⣤⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣟⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠀⠀⠈⠉⠉⠘⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢸⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡹⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⣀⣌⡙⣫⣀⣤⣤⣤⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠀⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣇⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⡿⠹⠿⠻⣿⣄⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣧⣦⡄⠩⣉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠟⣥⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⠀⠉⠉⠋⢰⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⡿⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢸⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡋⠏⣸⡙⡝⠝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⢀⣠⣀⠺⠿⢇⣤⣦⣶⣦⣶⣷⣶⣶⣶⣶⣿⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠉⠉⠀⠉⠁⠈⠉⠉⠁⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠾⠟⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣧⣦⡄⠉⢉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⢟⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠠⠄⠉⠉⠋⢰⣾⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢟⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⣿⠛⠉⢸⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⡋⠏⣸⡝⡝⠝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣿⣿⣿⣿⡗⣠⣤⣀⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣿⣿⣶⣭⣟⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠈⠉⠀⠉⠁⠉⠉⠉⠉⠉⠉⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠾⠿⢿⢟⣿⢿⣯⣯⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢩⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣯⣦⣚⢿⣷⠄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡾⣿⢣⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡟⣸⣿⣿⢳⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣷⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⠻⣿⣿⣛⢛⣸⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⣿⣿⣿⡽⣿⡿⠿⣧⣛⣛⣿⣭⣷⣿⣿⣿⣿⠿⣿⡧⡠⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⢉⡉⢉⣉⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⠋⠵⢾⣿⣿⣿⡿⠀⠀⠀⣤⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣟⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠉⠉⠉⠘⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢺⣿⣆⡤⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⣀⠬⠙⢋⣀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣾⣷⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⠶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣿⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣻⣾⣿⣇⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣯⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠙⢓⡡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣷⣦⡄⠉⢉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠟⣥⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⠀⠉⠉⠋⢱⣾⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡋⠏⣸⡙⡝⠽⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡗⢀⣀⣀⠺⠿⢇⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣭⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠾⠏⢿⢟⣿⢿⣯⣯⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠂⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢩⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣀⣠⣤⣔⡶⣶⣶⡄⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣾⣿⣿⣿⣿⣿⣿⣾⣿⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⢿⣹⡇⣧⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣮⣭⡭⣉⢑⡲⣭⢛⠷⡻⣆⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⡹⣫⣾⣏⢾⣿⢮⣗⢮⡤⢈⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣯⢎⣾⣿⣿⣿⣿⣮⣛⠙⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣣⣽⣾⣭⡻⣿⣿⣿⣁⣠⣭⣤⣤⡄⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢛⣻⣿⢣⣿⣿⣿⣿⠿⢹⡿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣷⣤⣍⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠻⢛⣜⠿⣿⠿⠏⠿⠷⢿⣎⣯⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣟⠿⣼⡇⣠⡄⠉⢉⡉⢉⣛⣻⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣝⡿⣿⣿⣿⣿⣿⣿⣿⣾⣝⢸⣿⣿⣿⣿⢸⣿⣿⣿⡿⣿⡿⠱⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠚⢙⣛⢿⣷⣝⠿⠿⢿⣷⣝⣛⣛⣵⣿⣿⣿⣿⠷⣈⣴⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣀⠙⠻⠿⠿⠿⣟⡉⠉⠉⠉⠉⠉⠉⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣿⡟⣵⣖⣊⣶⣤⡀⣸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢱⣿⣿⣛⢸⣿⠇⠾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠈⣛⠿⢟⣾⡟⠀⠻⠿⢟⣠⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠙⢛⢀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⣀⣀⣠⢤⣤⣤⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣵⣿⣿⣿⣿⣿⣿⣼⣿⠆⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⣻⡏⣧⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣭⣟⡛⢛⣙⣥⣼⠻⢧⢻⣆⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⢋⣾⣟⢾⣿⣯⡳⢥⡄⢉⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣟⢜⣵⣿⣿⣿⣷⣜⡛⠋⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⢫⣬⣭⣽⡻⣿⣿⣿⣁⣠⣭⣤⣤⡄⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⣛⣿⢧⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣷⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠿⢿⡜⢿⣿⣿⡏⣾⣷⣶⣎⣽⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠿⣸⡇⣤⡄⠉⢉⡉⢉⣛⣻⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⢿⣷⣶⣾⣿⣿⣿⣷⣯⡻⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠢⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡿⠷⠊⣻⣟⢿⣯⣻⢿⣿⡿⣮⣛⡿⣟⣫⣿⣿⣿⣿⡷⣈⣥⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢟⡀⠙⠿⠿⣿⡿⢿⡋⠉⠛⠛⠛⠋⠉⠁⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣰⣿⢷⣿⣽⡆⣦⣀⠀⠬⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⢸⣿⣿⡷⣿⣿⠗⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⣠⣭⣿⣵⣿⡟⠀⠙⠛⣫⣠⣤⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠉⢉⢀⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⣀⣀⣠⠤⣤⣤⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣵⣿⣿⣿⣿⣿⣿⣼⣿⠇⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⣻⡏⣧⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣭⣟⡛⢛⢙⣥⣼⠻⢧⢻⣆⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⢋⣾⣟⢾⣿⣯⡳⢥⡄⢉⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣟⢝⣵⣿⣿⣿⣷⣔⡛⠋⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⢋⣬⣭⣽⡻⣿⣿⣿⣁⣠⣭⣤⣤⡄⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⣛⣿⢧⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣷⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠿⢿⡜⢿⣿⣿⡏⣾⣷⣶⣎⣽⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠿⣸⡇⢠⡄⠉⢉⡉⣉⣛⣻⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⢿⣷⣶⣾⣿⣿⣿⣶⣮⡻⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠢⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠷⠊⣻⣟⢿⣯⣻⢿⣿⡿⣮⣛⡿⢟⣫⣿⣿⣿⣿⡷⣈⣥⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢟⡀⠙⠿⠿⣿⡿⢿⡋⠉⠛⠛⠛⠋⠉⠁⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣰⣿⢷⣿⣽⡆⣦⣀⠀⠬⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⢸⣿⣿⡷⣿⣿⠗⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⣠⣭⣿⣵⣿⡟⠀⠙⠛⣫⣠⣤⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠉⢉⢀⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣀⣀⣀⣠⠤⣤⣤⡄⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣵⣿⣿⣿⣿⣿⣿⣽⣿⠇⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⡿⣻⡏⣧⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣭⡟⡛⣛⣙⣥⣼⠻⢧⢻⣆⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢏⣬⣾⣟⢾⣿⣿⡳⢥⡄⢉⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⡟⣵⣿⣿⣿⣿⣷⣜⡛⠋⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣽⣇⢿⣿⣿⣿⣿⣿⣿⣁⣠⣭⣤⣤⡄⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⣻⣿⣷⣽⣷⣶⣾⣯⣭⣭⣛⠿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣷⣤⣍⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠿⢿⣿⣿⣿⣿⣧⡻⣿⣿⣿⢿⣮⣛⣿⣛⣱⣿⣿⣿⣿⣿⣿⡿⠿⣸⡧⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠢⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠷⠊⣻⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣈⣥⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢟⡀⠀⠠⢉⠻⢏⣭⡍⠉⠛⠛⠛⠋⠉⠁⠀⠟⠛⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣰⣿⢷⣿⣽⡆⣦⣀⠀⠬⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⢸⣿⣿⡷⣿⣿⠗⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⣭⣿⣵⣿⡟⠀⠙⠛⣫⣠⣤⣶⣶⣶⣶⣶⣾⣾⣶⣶⣿⣿⣿⣶⣭⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠉⣉⢀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⣀⣀⣠⢤⣤⣤⠄⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣵⣿⣿⣿⣿⣿⣿⣽⣿⠇⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣻⡏⣧⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣭⡟⡛⣛⢙⣥⣼⠻⢧⢻⣆⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢏⣬⣾⣟⢾⣿⣿⡳⢥⡄⢉⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⡟⣵⣿⣿⣿⣿⣷⣜⣛⠋⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣻⣇⢿⣿⣿⣿⣿⣿⣿⣁⣠⣭⣤⣤⡄⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⣛⣿⣷⣽⣷⣶⣾⣯⣭⣭⣛⠿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣤⣍⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠿⢿⣿⣿⣿⣿⣧⡻⣿⣿⣿⢿⣮⣛⣻⣛⣵⣿⣿⣿⣿⣿⣿⡿⠿⣸⡧⣦⡄⠉⢉⡉⣉⣛⣽⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠢⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠷⠊⣻⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢈⣥⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢟⡀⠀⠂⠉⠻⢏⣭⡍⠉⠛⠛⠛⠋⠉⠁⠀⠛⠛⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣰⣿⣷⣿⣽⡆⣦⣀⠀⠬⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⢸⣿⣿⡷⣿⣿⠗⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⣭⣿⣵⣿⡟⠀⠙⠛⣫⣤⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣿⣾⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠉⢉⢀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣯⣶⣚⢿⣷⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⣻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⠿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣷⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣿⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⢯⣛⣛⣿⣭⣷⣿⣿⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣙⣹⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⣻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⡟⠋⠵⣾⣿⣿⣿⡿⠀⠀⠀⣴⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠉⠀⠉⠉⠉⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⢀⣀⣈⠙⣋⣠⣤⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣬⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠉⠉⠀⠉⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⡶⠶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣀⢤⣾⡄⠘⠛⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⡿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣙⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠐⣀⠉⠉⠋⢰⣿⣷⡉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡋⠏⣸⡝⡝⡽⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⣠⣤⣀⠺⠿⢇⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠈⠉⠉⠉⠉⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣯⣶⣚⢿⣷⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⢳⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠿⣿⠴⠿⠛⠵⣿⣿⣷⡙⡿⠿⠾⢟⣧⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢩⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣿⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠈⠉⡉⢉⣉⣩⣹⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⠋⠵⢾⣿⣿⣿⡿⠀⠀⠀⣴⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠈⠉⠉⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢸⣿⣆⡦⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⢀⣀⣈⡙⢋⣠⣤⣴⣤⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡶⢶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢃⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠗⣡⣶⣿⣷⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⠂⠉⠉⠋⢰⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠁⠈⡏⠏⣸⡝⡝⡽⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⢠⣤⣄⠺⠿⢇⣤⣶⣶⣾⣷⣾⣷⣶⣶⣶⣷⣾⣷⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠈⠀⠈⠉⠉⠉⠁⠈⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢉⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡼⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⣻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣧⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣿⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣟⣛⢛⣾⣿⣯⣭⣭⡁⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣧⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣋⣟⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⢋⠵⢾⣿⣿⣿⠿⠀⠀⠀⣴⣴⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠈⠉⠉⠘⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢸⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⢠⣄⢨⡙⣫⣤⣤⣤⣴⣶⣦⣶⣶⣶⣶⣶⣶⣶⣷⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⡶⢶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣫⣾⣿⣃⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣁⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠟⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠗⣥⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⢂⢉⠉⠋⢰⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢸⣿⣧⢶⡬⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡋⠏⣸⡙⡝⠝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⣠⣦⣄⠺⠿⢇⣴⣾⣶⣾⣶⣿⣷⣶⣶⣶⣿⣿⣿⣶⣭⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠉⠉⠉⠉⠁⠉⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠾⠏⠿⢟⣿⢿⣯⣯⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢉⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡼⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⣻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⠿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣧⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢘⣛⡓⣒⣿⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣟⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣧⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⢉⡉⢉⣉⣽⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⡟⠋⠵⢾⣿⣿⣿⠿⠀⠀⠀⣴⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠉⠉⠉⠘⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢸⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⢀⡄⣨⡙⣫⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠈⠈⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⠶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣻⣾⣿⣃⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣁⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠟⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡇⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠵⠿⠿⠿⠿⠿⠗⣡⣶⣿⣷⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠠⠀⠉⠉⠋⢸⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⡛⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⡿⠛⠉⢸⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡋⠏⣸⡝⡝⠝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⢠⣤⣄⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣿⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠉⠉⠈⠉⠁⠉⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢹⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣷⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⡶⠤⠤⣀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⠛⢑⣼⣿⡿⢷⣒⣀⡼⣿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⣴⣶⣶⣶⣽⣿⢯⣾⣿⣿⣿⣿⣮⢻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣯⣿⣿⣿⣿⢿⣿⢸⣿⣿⣿⣿⣷⣾⢿⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣟⢿⣿⣿⡿⠟⠿⠿⠿⠯⠻⣿⣿⣿⡿⣫⣾⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⠹⠶⠶⢵⣶⣛⣿⢹⣶⣿⣷⣶⣝⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⡼⠿⠷⣿⣟⡛⣛⣸⣿⣭⣭⡭⠁⠀⣭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢟⣵⣿⡿⢇⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢿⣟⣛⣛⣿⣿⣭⣬⡹⣷⣶⣶⣾⠿⣻⣾⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣩⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣯⢻⣿⡿⠞⣿⣛⣻⣿⣭⣽⣷⣾⣿⣿⣿⣿⡎⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣾⣿⢟⣛⡻⣿⣿⣿⣿⣟⡿⠿⠟⡋⠵⣾⣿⣿⣿⡿⠀⠀⠀⣤⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣾⣿⠇⠛⠛⠛⠉⠚⠸⣿⣷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠋⢰⣷⡆⣄⢠⣿⣿⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⢘⠝⡝⣴⣱⢱⠃⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⢸⣿⣿⣿⣿⣿⠀⣠⣌⡛⣛⣡⣤⣴⣴⣶⣦⣶⣶⣶⣶⣶⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⡶⠤⠤⣀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⠛⢙⣼⣿⡿⢷⣒⣀⡼⣿⣷⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⣴⣶⣶⣶⣽⣿⢏⣾⣿⣿⣿⣿⣮⢻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣾⣯⣿⣿⣿⣿⢷⣿⢸⣿⣿⣿⣿⣷⣾⢿⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣿⣿⣿⡿⠟⠿⠿⠿⠯⠻⣿⣿⣿⡿⣫⣾⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⠹⠶⠶⢵⣶⣛⣿⢹⣶⣿⣷⣶⣝⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⡼⠿⠷⣿⣟⡛⣛⣸⣿⣭⣭⡭⠁⠀⣭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢟⣵⣿⡿⢇⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢿⣟⣛⣛⣿⣿⣭⣬⡹⣷⣶⣶⣾⠿⣻⣾⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣩⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣯⢻⣿⡿⠞⣿⣛⣛⣿⣭⣽⣷⣾⣿⣿⣿⣿⡎⣫⣾⣿⣿⡞⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣾⣿⢟⣛⡻⣿⣿⣿⣿⣟⡿⠿⠟⡋⠵⣾⣿⣿⣿⠿⠀⠀⠀⣤⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣾⣿⠇⠛⠛⠛⠉⠚⠸⣿⣷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⡿⠟⠋⢰⣷⡄⣄⢠⣿⣿⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢘⠝⡝⣽⣱⢱⠃⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⢀⣤⣌⡛⡛⣡⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠈⠁⠁⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⢶⣶⣶⠖⠒⠢⢤⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠋⣩⣾⣿⡿⣓⣶⣦⣸⢿⣿⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣫⣶⣶⣶⣿⣼⣿⢫⣾⣿⣿⣿⡿⢷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⣿⣿⣿⢻⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢿⣿⡿⠿⠛⠵⢿⣿⣷⠝⠿⠿⡿⢿⣫⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢐⣻⡖⣐⣲⣯⣽⢱⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣾⣟⣓⣛⣻⡟⣭⣬⣭⣽⡷⢶⣀⠀⣭⣤⣤⣄⠲⠆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⣋⣞⣛⣛⢣⣿⣟⠻⣿⡗⡸⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡫⣭⣽⣯⣳⣶⣶⣿⣞⢿⡿⠿⣿⣻⣵⣿⡻⢿⣿⡎⣽⣷⢹⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣭⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣝⣟⣛⣷⣭⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢆⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣿⡻⣿⣿⣿⡿⣫⠿⣟⠛⠉⡲⠿⢿⣿⡿⠟⠀⠀⠀⣴⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⣿⠃⠉⠉⠉⠚⣛⡸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢸⣿⣦⠀⡴⣿⡿⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⢈⡋⠏⣰⣜⡘⠁⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⣿⣿⣿⡇⢠⠤⣍⣛⣋⣠⣤⣶⣤⣴⣦⣶⣶⣶⣶⣶⣶⣾⣷⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⢶⣶⣶⡖⠒⠢⢤⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠋⣩⣾⣿⡿⣓⣶⣦⣸⢿⣿⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣯⣶⣶⣶⣿⡼⣿⢫⣾⣿⣿⣿⡿⢷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⣿⣿⣿⢻⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢿⣿⡿⠿⠛⠵⢿⣿⣷⠝⠿⢿⡿⢿⣫⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢐⣻⡖⣐⣲⣯⣽⢱⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣾⣟⣓⣛⣿⡟⣭⣬⣭⣿⡿⢶⣀⠀⣭⣤⣤⣄⠲⠆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠫⠾⠿⣿⢇⣿⣟⠻⣿⡗⡸⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢛⣻⣿⣍⢭⣽⣿⣶⡴⣶⣿⣿⡿⣟⣯⣾⡻⢿⣿⡎⣽⣷⢹⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣙⣽⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣷⡻⠿⢿⣏⣛⣿⣯⣭⣾⣶⣾⣿⣿⣿⣿⣿⢆⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣿⡻⣿⣿⣿⣿⢏⠿⣟⠛⠉⡲⠿⢿⣿⡿⠟⠀⠀⠀⣴⣶⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣿⠃⠛⠛⠋⠑⣛⡸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢸⣿⣦⠀⡴⣿⡿⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⢈⡋⢏⣰⣜⡘⠁⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⣿⣿⣿⡇⠀⢀⣍⣛⢋⣠⣤⣤⣤⣶⣦⣶⣶⣶⣶⣦⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠉⠁⠀⠉⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⢶⣶⣶⠖⠒⠢⢤⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠋⣹⣾⣿⡿⣓⣶⣦⣺⢿⣿⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣫⣶⣶⣶⣷⣼⣿⢫⣾⣿⣿⣿⡿⢷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⣿⣿⣿⢳⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢿⣿⡿⠿⠛⠵⢿⣿⣷⠝⠿⠿⡿⢿⣫⣿⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢐⣿⡗⣐⣲⣯⣽⢱⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣾⣟⣓⣛⣿⡟⣭⣬⣭⣽⡷⠶⣀⠀⣭⣤⣤⣄⠲⠆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠯⠾⠿⣿⢇⣿⣟⠻⣿⡗⡸⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣁⠼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢛⣻⣿⣍⢭⣭⣿⣶⡴⣶⣿⣿⡿⣟⣯⣾⡻⢿⣿⡎⣽⣷⢹⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣙⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣷⡻⠿⢿⣏⣛⣿⣯⣭⣶⣶⣾⣿⣿⣿⣿⣿⢆⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣿⡻⣿⣿⣿⣿⢏⠿⣟⠛⠉⡲⠿⢿⣿⡿⠟⠀⠀⠀⢤⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⣿⠃⠛⠛⠋⠑⣛⡸⣿⣷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢸⣿⣦⠀⡴⣿⡿⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⢈⡋⢏⣰⣜⡘⠁⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⣉⣛⢋⣤⣤⣤⣶⣴⣦⣦⣦⣶⣶⣤⣴⣶⣴⣴⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⢶⣶⣶⠖⠒⠢⢤⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠋⣹⣾⣿⡿⣓⣶⣦⣺⢿⣿⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣯⣶⣶⣶⣿⣼⣿⢫⣾⣿⣿⣿⡿⢷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⣿⣿⣿⢳⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢿⣿⡿⠿⠛⠵⢿⣿⣷⠝⠿⢿⡿⢿⣫⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢐⣿⡗⣐⣲⣯⣽⢱⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣾⣟⣓⣛⣻⡟⣭⣬⣭⣽⡷⢦⣀⠀⣭⣤⣤⣄⠲⠆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⣋⣾⣛⣛⢣⣿⣟⠻⣿⡗⡸⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣁⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡩⣭⣭⣯⣳⣶⣶⣿⣞⢿⡿⠿⣟⣻⣵⣿⡻⢿⣿⡎⣽⣷⢹⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣉⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣝⣟⣛⣷⣭⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢆⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣿⡻⣿⣿⣿⡿⣣⠿⣟⠛⠉⡲⠿⢿⣿⡿⠟⠀⠀⠀⢴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⣿⣿⠃⠉⠉⠉⠚⣛⡸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢸⣿⣦⠀⡴⣿⡿⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⢈⡋⢏⣰⣜⡘⠁⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⣉⣛⢋⣤⣤⣶⣴⣶⣦⣶⣴⣶⣶⣶⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠋⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⢶⣶⣶⠖⠒⠠⢤⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠋⣹⣾⣿⡿⣓⣶⣦⣺⢿⣿⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣫⣶⣶⣶⣿⣼⣿⢫⣾⣿⣿⣿⡿⢷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⣿⣿⣿⢳⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢿⣿⡿⠿⠛⠵⢿⣿⣷⠝⠿⢿⡿⢿⣫⣿⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢐⣿⡗⣐⣲⣯⣽⢱⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣾⣟⣓⣛⣻⡟⣭⣬⣭⣽⡷⢦⣀⠀⣭⣤⣤⣄⠲⠆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⣋⣞⣛⣛⢣⣿⣟⠻⣿⡗⡸⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡩⣭⣭⣯⣳⣶⣶⣿⣞⢿⡿⠿⣟⣻⣵⣿⡻⢿⣿⡎⣽⣷⢹⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣙⣙⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣝⣟⣛⣷⣭⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢆⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣿⡻⣿⣿⣿⡿⣣⠿⣟⠛⠉⡲⠿⢿⣿⡿⠟⠀⠀⠀⣤⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⣿⠃⠉⠉⠉⠚⣛⡸⣿⣷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢸⣿⣦⠀⡴⣿⡿⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⢈⡋⢏⣰⣜⡘⠁⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⣩⡛⣋⣤⣴⣴⣴⣶⣦⣶⣴⣶⣶⣤⣴⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⢶⣶⣶⠖⠒⠢⢤⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠋⣹⣾⣿⡿⣓⣶⣦⣺⢿⣿⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣫⣶⣶⣶⣿⣼⣿⢫⣾⣿⣿⣿⡿⢷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⣿⣿⣿⢳⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢿⣿⡿⠿⠛⠵⢿⣿⣷⠝⠿⢿⡿⢿⣫⣿⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢐⣿⡗⣐⣲⣯⣽⢱⣿⣿⣿⣷⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣾⣟⣓⣛⣻⡟⣭⣬⣭⣿⡷⢦⣀⠀⣭⣤⣤⣄⠲⠆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠫⠾⠿⣿⢇⣿⣟⠻⣿⡗⡸⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣁⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢛⣻⣿⣍⢭⣭⣿⣶⡴⣶⣿⣿⠿⣟⣯⣾⡻⢿⣿⡎⣽⣷⢹⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣙⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣷⡻⠿⢿⣏⣛⣿⣯⣭⣾⣶⣾⣿⣿⣿⣿⣿⢆⣫⣾⣿⣿⡾⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣿⡻⣿⣿⣿⣿⢏⠿⣟⠛⡉⡲⠿⢿⣿⡿⠟⠀⠀⠀⣦⣴⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⣿⣿⠃⠛⠛⠋⠑⣛⡸⣿⣷⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢸⣿⣦⠀⡴⣿⡿⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⢈⡋⢏⣰⣜⡘⠁⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢸⣿⣿⣿⣿⡇⠀⢀⣍⣛⣋⣤⣤⣤⣴⣶⣦⣶⣶⣶⣶⣦⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⠶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣿⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣻⣾⣿⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⡿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠟⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣧⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠏⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠁⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⡟⠀⠀⢀⢉⠉⠋⢰⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⣻⡛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⡏⠏⣸⡙⡝⡝⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⢀⣄⡀⡺⠿⢇⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠈⠈⠉⠉⠉⠀⠈⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣭⣴⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣶⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⣻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⣿⠿⠾⢟⣷⣿⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣟⣛⢛⣾⣿⣯⣭⣭⡅⣠⢩⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣋⣹⣯⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⡟⠋⠵⣾⣿⣿⣿⡿⠀⠀⠀⣴⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠈⠉⠉⠘⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⣨⡙⣉⣤⣤⣤⣤⣶⣦⣶⣶⣶⣶⣦⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣟⣯⣿⣷⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣫⣾⣿⣃⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢯⡿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣦⡄⠉⢉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠁⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠐⠆⡉⠉⠋⢰⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢛⡛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡄⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡏⠏⣸⡙⡝⡝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡗⣠⣄⣀⠺⠿⢇⣤⣷⣶⣶⣷⣶⣶⣶⣶⣶⣾⣿⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠈⠉⠉⠉⠉⠁⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠩⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣿⣷⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣇⣿⣻⣾⣿⣃⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣤⡄⠉⢉⡉⣉⣛⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⡀⠉⠉⠋⢰⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⡛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢸⣿⣧⢶⡄⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⡏⠏⣸⡙⡝⡽⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡗⢠⣤⣀⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠺⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡟⣸⣿⣿⣳⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⠿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣧⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣧⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⠉⡉⢉⣉⣙⣫⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡜⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⠋⠵⢾⣿⣿⣿⡿⠀⠀⠀⢤⣴⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠉⠉⠉⠘⣿⣿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢺⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⠀⡀⣨⡙⢫⣤⣤⣠⣤⣶⣦⣶⣶⣶⣶⣦⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⠶⣶⠶⠒⠤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣿⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣫⣾⣿⣃⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠽⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣁⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠗⣠⣶⣿⣷⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠈⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠠⡀⠉⠉⠋⢰⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⡿⠛⠉⢸⣿⣧⢶⡄⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡏⠏⣸⡝⡝⡝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⡇⣠⣤⣀⠺⠿⢇⣤⣶⣶⣾⣶⣶⣾⣶⣾⣶⣿⣿⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠈⠉⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⠄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⣻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⠿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣧⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢳⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣧⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢠⡄⠈⠉⡉⢉⣉⣉⣯⣽⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡞⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⡟⢋⠵⢾⣿⣿⣿⡿⠀⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠉⠉⠉⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⡦⣰⣿⡗⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⠨⡙⣉⣤⣦⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣾⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⡀⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠿⠿⠓⢿⡝⠻⣿⡿⠿⣿⣶⣄⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣫⡶⣿⣷⣤⣤⡰⣿⣷⣠⣤⣤⣾⣗⣮⡻⡧⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢳⣿⣿⣿⣿⣿⣿⣷⣿⣧⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣿⣿⣿⣥⣬⣍⣤⣤⣤⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣮⣻⡿⠿⣟⣯⠞⣻⣛⡊⢛⣛⡿⢟⣯⣾⣿⣿⣿⣿⣷⡔⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣷⣾⣿⣯⣿⣾⣷⡽⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⡇⢦⡄⠉⢉⡉⢉⣹⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣟⢿⣿⣿⡇⣿⣿⣿⣿⣿⣛⠿⠸⠿⠿⠿⠿⠿⠗⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣡⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣷⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣷⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣻⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢿⡿⢫⣿⣿⣭⣯⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣭⣿⣿⣯⣝⠿⠁⠀⠀⠛⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣻⠿⣿⣿⣿⣟⣿⣷⣝⣛⣛⣯⣿⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⣣⡿⠍⣩⣬⠙⠛⠟⣻⣟⠩⣭⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⢿⢿⠇⣤⡸⡿⡿⠀⠀⢹⣷⡠⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣴⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠼⠿⠗⠀⠀⢨⣬⠴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣾⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠿⠿⠓⢿⡝⠻⣿⡿⠿⣿⣶⣄⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣫⡶⣿⣷⣤⣤⡰⣿⣷⣠⣤⣤⣾⣗⣮⡻⡧⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢳⣿⣿⣿⣿⣿⣿⣷⣿⣧⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣿⣿⣿⣥⣬⣍⣤⣤⣤⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣮⣻⡿⠿⣟⣯⠞⣛⣛⡊⢛⣛⡿⢟⣯⣾⣿⣿⣿⣿⣷⡐⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣷⣾⣿⣭⣿⣾⣷⡽⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⡇⣠⡄⠉⠉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣟⢿⣿⣿⡇⣿⣿⣿⣿⣿⣛⠿⠸⠿⠿⠿⠿⠿⠗⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣡⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣷⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⡷⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢿⡿⢫⣿⣿⣭⣯⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣧⣿⣿⣯⣝⠿⠁⠀⠀⠛⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣻⠿⣿⣿⣿⣟⣿⣷⣝⣛⣛⣯⣿⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⣣⡿⠍⣩⣬⠙⠛⠿⣻⣟⠩⣬⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⢿⢿⠇⣤⡸⡿⡿⠀⠀⠹⣷⡠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣷⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠼⠿⠗⠀⠀⢨⣬⠴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠂⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⠿⠿⠿⠛⣪⡕⠲⠿⠿⠿⠿⣷⣄⠈⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣹⣞⣿⣷⣶⣶⡸⣿⡿⣢⣤⣴⣾⣿⣾⡻⠷⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢏⣿⣏⢿⣿⣿⣿⣥⣬⢍⣤⣤⣤⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣮⣝⣻⣿⣛⡵⡛⢯⣍⣁⣉⣽⣛⡻⣵⣿⣿⣿⣿⣿⣷⡔⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣷⡶⣶⣶⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⢠⡄⠉⢉⡉⣉⣛⣹⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣯⢻⣿⣿⡇⣿⣿⣿⣿⣿⣝⠻⠸⠿⠿⠿⠿⠿⠗⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣵⣿⣿⣿⡟⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣻⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡻⡿⣣⣿⣿⣮⣽⣾⣿⡿⣿⣿⣿⣿⣿⣷⣭⣵⣿⣿⣷⣍⠛⠁⠀⠀⠛⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣟⡿⢿⣿⣿⣏⢿⣷⣯⣟⣻⣵⣿⢿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⢟⣧⡶⠞⣩⣥⠉⠛⠛⣿⣏⠱⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⢿⢿⠇⣦⡸⡿⡿⠀⠀⢹⣷⡠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣾⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠜⠿⠗⠀⠀⢨⣬⠴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⡿⠿⠿⠛⣪⡕⠺⠿⠿⠿⠿⣷⣄⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣹⣞⣿⣷⣶⣶⡸⣿⡿⣢⣤⣴⣾⣿⣾⡻⡷⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢏⣿⣏⢿⣿⣿⣿⣥⣬⢍⣤⣤⣤⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣮⣝⣻⣿⣛⡵⡛⢯⣍⣁⣉⣿⣛⡻⣵⣿⣿⣿⣿⣿⣷⡜⣶⣶⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣷⣶⣶⣶⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣇⣤⡄⠉⢉⡉⣉⣛⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⢻⣿⣿⡇⣿⣿⣿⣿⣿⣝⠻⠸⠿⠿⠿⠿⠿⠗⣠⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣵⣿⣿⣿⡟⣿⣿⢿⣿⣿⣿⣷⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣻⡿⣣⣿⣿⣮⣽⣾⣿⡿⣿⣿⣿⣿⣿⣷⣭⣵⣿⣿⣷⣍⠛⠁⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣟⡿⢿⣿⣿⣏⢿⣷⣭⣟⣻⣵⣿⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⢟⣯⡶⠞⣩⣥⠉⠛⠛⣿⣏⠱⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⢿⢿⠇⣦⠸⡿⡿⠀⠀⢹⣷⡠⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠼⠿⠗⠀⠀⢨⣬⠴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⠿⠿⠿⠛⣪⡕⠺⠿⠿⠿⢿⣷⣄⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣹⣞⣿⣷⣶⣶⡸⣿⡿⣢⣤⣴⣿⣿⣾⡿⡷⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢏⣿⣏⢿⣿⣿⣿⣥⣬⢍⣤⣤⣤⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣮⣝⣻⣟⣛⡵⡛⢯⣍⣁⣉⣽⣛⡻⣵⣿⣿⣿⣿⣿⣿⡔⣶⣶⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣷⣶⡶⣶⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⣤⡄⠉⢉⡉⣉⣛⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⢻⣿⣿⡇⣿⣿⣿⣿⣿⣝⠻⠸⠿⠿⠿⠿⠿⠇⣠⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣵⣿⣿⣿⡟⣿⣾⢿⣿⣿⣿⣷⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣻⡿⣣⣿⣿⣮⣽⣾⣿⡿⣿⣿⣿⣿⣿⣷⣭⣵⣿⣿⣷⣍⠛⠁⠀⠀⠛⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣟⡿⢿⣿⣿⣏⢿⣷⣯⣟⣻⣵⣿⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⢟⣯⡶⠞⣩⣥⠉⠛⠛⣻⣏⠱⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⢿⢿⠇⣦⡸⡿⡿⠀⠀⢹⣷⡠⣤⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠼⠿⠗⠀⠀⢨⣬⠴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⡿⠿⠿⠛⣪⡕⠚⠿⠿⠿⠿⣷⣄⠈⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣽⣞⣿⣷⣶⣶⡸⣿⡿⣢⣤⣴⣿⣿⣾⡿⡷⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⢏⣿⣏⢿⣿⣿⣿⣥⣬⢍⣤⣤⣤⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠙⢊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣝⣻⣿⣛⡵⡛⢯⣍⣁⣉⣽⣛⠻⣵⣿⣿⣿⣿⣿⣿⡔⣶⣶⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣷⡶⣶⣶⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣧⣦⡄⠉⠉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⡇⣿⢻⣿⣿⡇⣿⣿⣿⣿⣿⣝⡻⠸⠿⠿⠿⠿⠿⠗⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣵⣿⣿⣿⡟⣿⣾⢿⣿⣿⣿⣷⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⡿⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡻⡿⣡⣿⣿⣮⣽⣾⣿⣿⣿⣿⣿⣿⣿⣷⣭⣵⣿⣿⣷⣍⠛⠁⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣟⡿⢿⣿⣿⣏⢿⣷⣯⣟⣻⣵⣿⢻⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⢟⣭⡶⠞⣩⣥⠉⠛⠛⣻⣏⠱⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⢿⢿⠇⣶⡸⡿⡿⠀⠀⢹⣷⡠⣴⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠼⠿⠗⠈⠀⢨⣬⠴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠉⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣿⣾⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⡿⠹⠿⠻⣿⣄⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣁⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣎⡝⡐⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⡳⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣇⣦⡄⠉⢉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠟⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠀⡴⢉⠙⠃⢰⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⢀⠟⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡄⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡏⠏⣸⡙⡝⠽⠑⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡗⣀⣤⣄⠾⠿⢇⣴⣶⣶⣶⣶⣶⣶⣷⣶⣶⣿⣿⣿⣶⣭⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠉⠉⠀⠈⠁⠉⠉⠉⠁⠁⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠯⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣿⣦⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⡿⣿⠴⠿⠛⠵⣿⣿⣷⡙⣿⠿⠾⢟⣷⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣯⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢷⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡷⠠⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⣠⡄⠉⠉⡉⢉⣛⣻⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣽⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⠋⠵⢾⣿⣿⣿⡿⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠀⠀⠀⠈⠉⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⡶⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠄⣀⡨⡙⢩⣤⣤⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣿⣦⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣿⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⣿⠿⠾⢟⣷⣿⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢜⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢷⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⣿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡷⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⣠⡄⠉⠉⡉⢉⣻⣽⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⢋⠵⣾⣿⣿⣿⡿⠀⠀⠀⣴⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠀⠈⠉⠘⣿⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁⢾⣿⣆⡶⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⣀⡈⠙⢉⢄⣠⣤⣤⣴⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣷⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢯⡿⠽⠿⠻⣿⣄⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣑⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣎⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠙⢓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣷⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣧⣦⡄⠉⠉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠵⠿⠿⠿⠿⠿⠟⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠐⠄⠨⡙⠋⢰⣿⣿⡉⠁⠀⠈⠀⠀⠀⠀⠀⠛⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠉⢰⣿⣧⢶⡌⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡏⠏⣸⡙⡝⠽⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡗⣀⣠⣄⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣭⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠉⣩⣾⣿⢿⣻⣿⣦⣚⢿⣷⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣿⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣷⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⣿⠿⠾⢟⣷⣿⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣭⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢷⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠁⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⣿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡷⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⠉⡉⢉⣛⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣽⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⢋⠵⣾⣿⣿⣿⡿⠀⠀⠀⣤⣴⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠀⠀⠀⠈⠉⠘⣿⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢺⣿⣆⡶⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡱⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⠀⠀⠨⠙⢫⣠⣀⣦⣤⣦⣶⣴⣴⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠲⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣧⣿⣻⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⡿⠽⠿⠻⣿⣄⢻⣿⣷⣮⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣙⠾⠏⢋⣴⣿⣿⣿⣿⣿⣧⣎⡝⡔⡰⠋⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠙⢓⡮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢾⣿⣷⢶⣿⣷⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣷⣦⡄⠉⢉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⢟⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣴⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠐⠠⠠⠈⠙⠋⢱⣾⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⡿⠛⠉⢰⣿⣧⢶⡄⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⡋⠏⣸⡙⡝⠽⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡗⣠⣀⣀⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⠿⠟⠒⣭⠒⠽⠿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣿⣿⣗⣤⡤⣾⣿⣷⢦⣰⣿⣭⣽⣟⢷⡀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢯⣷⣿⣿⣿⣿⣿⣿⣷⣿⢳⣿⣿⣿⣯⣿⣿⣷⣧⡀⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⢿⣿⣿⣿⣿⣿⠿⣋⣛⡋⠛⠛⡛⢛⣛⣻⠵⣹⣿⡿⢂⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⣟⣓⣒⣶⣶⣿⣬⣇⡿⢭⣥⣿⢟⣵⣿⣿⣿⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣦⢶⣹⣿⣿⣿⣁⣠⣭⣤⣤⣀⡒⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢃⣿⣿⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⠉⡉⢉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⠿⠿⠿⠿⠿⠿⠿⠟⣠⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⡻⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⠉⠀⠀⠉⠈⠀⠀⠀⣴⣶⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣻⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣭⢍⣶⣶⠙⠛⠛⠛⠛⠋⠑⣶⣾⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠏⢠⣶⡄⣀⢀⣶⣶⠈⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣟⠁⠀⠘⢟⢟⢸⠘⡟⠟⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⣿⡦⠀⠀⣷⣶⣿⣷⣶⠀⢀⣀⢛⡛⣡⣤⣠⣠⣤⣶⣦⣶⣶⣶⣴⣶⣶⣾⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠈⠁⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⠿⠟⠒⣭⠒⠽⠿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⣿⣿⣗⣤⡤⣾⣿⣷⢦⣰⣿⣯⣽⣟⢷⡀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢯⣶⣿⣿⣿⣿⣿⣿⣷⣿⢳⣿⣿⣿⣯⣿⣿⣷⣧⣀⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⢿⣿⣿⣿⣿⣿⠿⣋⣛⡋⠛⠛⡛⢛⣛⣻⠵⣹⣿⡿⢂⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⣟⣓⣒⣶⣶⣿⣬⣇⡿⢭⣥⣿⢟⣵⣿⣿⣿⠟⣡⣶⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣦⢶⣹⣿⣿⣿⣁⣠⣭⣤⣤⣀⡒⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠁⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢃⣿⣿⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⠉⡉⣉⣿⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣷⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⡻⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠉⠐⠀⠀⠀⣴⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣭⢍⣶⣶⠙⠛⢛⠛⠛⠋⠑⣶⣾⣆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠟⢠⣶⡄⣂⣀⣶⣶⠈⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣿⠁⠀⠘⢟⢟⢸⠘⡟⠟⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡦⠀⠀⣷⣶⣿⣷⣶⠀⢀⣀⢛⡛⢡⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠈⠁⠈⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠤⣒⠬⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣯⣀⣀⣴⣿⣦⣤⢤⣟⣛⣛⡿⣦⠀⠀⠀⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣯⣷⣾⣿⣿⣿⣷⣏⣿⢯⣾⣿⣿⣟⣿⣿⣯⣇⠀⠁⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠟⠿⠜⠿⠿⠿⠿⠿⣿⣣⢫⣿⡶⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⠾⠭⠭⣭⣭⣿⣐⡏⣿⣓⣂⣶⡿⣪⣿⣶⣶⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣍⣭⢺⣿⣿⣿⣁⣠⣭⣤⣤⡠⠦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣟⡻⠟⣾⣿⣿⣿⣿⣿⣿⣿⡇⣦⡄⠉⠉⡉⣉⣟⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣜⢿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⠿⠛⠁⠀⠛⠂⠀⠀⠀⣤⣶⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣽⣛⢋⣶⣶⠹⠿⠟⠛⠻⠿⠃⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠟⢠⣶⡄⣐⡂⣴⣶⠈⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣟⠁⠀⠘⢟⣟⢸⡹⡹⡽⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⣿⡦⠀⠀⣷⣶⣿⣿⣶⠀⠀⣀⡍⣛⣭⣤⣴⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠁⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠤⣒⠬⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡯⣀⣀⣴⣿⣦⣤⢤⣟⣛⣛⡿⣦⠀⠀⠀⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣯⣷⣾⣿⣿⣿⣷⣏⣿⢯⣾⣿⣿⣟⣿⣿⣯⣇⠀⠁⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠟⠿⠜⠿⠿⠿⠿⠿⣿⣣⢫⣿⡶⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣗⠾⠭⠭⣭⣭⣿⣐⡏⣿⣓⣂⣶⡿⣪⣿⣶⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣍⢭⢺⣿⣿⣿⣁⣠⣭⣤⣤⡠⠦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣟⡻⠟⣾⣿⣿⣿⣿⣿⣿⣿⡇⣦⡄⠉⢉⡉⣉⣋⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⠿⠿⠿⠿⠿⠿⠿⠗⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⢿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⠿⠛⠁⠀⠈⠉⠀⠀⠀⣴⣴⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣽⣛⢋⣶⣶⠹⠿⠟⠛⠛⠿⠃⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠏⢠⣶⡄⣀⡀⣴⣶⠈⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣟⠁⠀⠘⢟⣟⢸⡹⡹⡽⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⣷⣶⣿⣿⣶⠀⣀⡀⡍⡛⣭⣤⣤⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠀⠀⠀⠉⠀⠈⠁⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠤⣒⠬⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡯⣀⣀⣴⣿⣦⣤⢤⣟⣛⣛⡿⣦⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣯⣷⣾⣿⣿⣿⣷⣏⣿⢯⣾⣿⣿⣟⣿⣿⣯⣇⠀⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠟⠿⠜⠿⠿⠿⠿⠿⣿⣣⢻⣿⡶⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⠾⠭⠭⣭⣭⣿⣒⡛⢿⣒⣆⣶⠷⣮⣿⣶⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣦⢮⣹⣿⣿⣿⣁⣠⣭⣤⣤⡠⠦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣾⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠟⣾⣿⣿⣿⣿⣿⣿⣿⡇⣦⡄⠉⠉⡉⣉⣋⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⠿⠿⠿⠿⠿⠿⠿⠗⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣜⢿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠿⠛⠁⠀⠙⠙⠀⠀⠀⣤⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣽⣛⢋⣶⣶⠹⠿⠟⠛⠛⠿⠃⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠏⢠⣶⡌⣀⡀⣴⣶⠈⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣟⠁⠀⠘⢟⣟⢸⡽⡹⡽⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⣷⣶⣿⣿⣶⠀⠀⣀⣍⡛⣭⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠤⣒⠬⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣀⣀⣴⣿⣦⣤⢤⣟⣛⣛⡿⣦⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣯⣷⣾⣿⣿⣿⣷⣏⣿⢯⣾⣿⣿⣟⣿⣿⣯⣇⠀⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠟⠿⠞⠿⠿⠿⠿⠿⣿⣣⢫⣿⡶⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⠾⠭⠭⣭⣭⣿⣐⡏⣿⣓⣂⣶⡿⣪⣿⣶⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣍⣭⢺⣿⣿⣿⣁⣠⣭⣤⣤⡠⠦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣿⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣟⡻⠟⣾⣿⣿⣿⣿⣿⣿⣿⡇⣦⡄⠉⠉⡉⢉⣛⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⠿⠿⠿⠿⠿⠿⠿⠗⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣜⢿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠿⠛⠁⠀⠉⠛⠀⠀⠀⣴⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣽⣛⢋⣶⣶⠹⠿⠿⠛⠛⠿⠃⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠟⢠⣶⡌⣀⡀⣴⣶⠈⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣟⠁⠀⠘⢟⣟⢸⡽⡹⡽⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⣷⣶⣿⣿⣶⠀⢀⣀⣭⡛⣭⣤⣤⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠈⠀⠈⠉⠀⠈⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠤⣒⠤⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣯⢀⣀⣴⣿⣦⣤⢤⣟⣛⣛⡿⣦⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣯⣷⣾⣿⣿⣿⣷⣯⣿⢫⣾⣿⣿⣟⣿⣿⣯⣇⠀⠀⠀⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠟⣿⠞⠿⠿⠿⠿⠿⣿⣣⢻⣿⡶⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣗⠾⠭⠭⣭⣭⣿⣐⡏⣿⣓⣂⣶⡿⣪⣿⣶⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣍⣭⢺⣿⣿⣿⣁⣠⣭⣤⣤⡠⠦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣶⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣟⡻⠟⣾⣿⣿⣿⣿⣿⣿⣿⡇⣦⡄⠉⢉⡉⣉⣛⣿⣻⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⣿⡿⠿⠿⠿⠿⠿⠿⠗⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣜⢿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⠿⠛⠁⠀⠉⠊⠀⠀⠀⣶⣶⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣽⣛⢋⣶⣶⠹⠿⠿⠛⠻⠿⠃⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⣼⣿⠏⢠⣶⡄⣀⡀⣴⣶⠈⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣟⠁⠀⠘⣟⣟⢸⡽⡹⡽⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢻⣿⡦⠀⠀⣷⣶⣿⣿⣶⠀⢀⣠⣍⣛⢭⣤⣴⣦⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠉⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠼⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣏⣿⣫⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣭⣶⣶⣶⣶⣿⣽⡻⢧⡿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣉⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠟⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣧⣢⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠟⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠖⢈⡉⡙⠋⢰⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣽⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠉⢸⣿⣧⢶⡄⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡏⠏⣸⡙⡝⠝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡖⣀⣠⣀⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠉⠁⠈⠉⠁⠉⠉⠉⠁⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠲⠤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣀⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢎⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣫⣾⣿⣃⢹⣿⡏⣼⢃⠎⡝⢿⣿⣶⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢯⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣁⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠟⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠙⢛⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣷⣦⡄⠉⢉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠵⠿⠿⠿⠿⠿⠟⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⡟⠀⠢⠌⠭⠙⠋⢰⣿⣿⠉⠁⠀⠈⠀⠀⠀⠀⠀⠿⠿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠉⢸⣿⣧⢶⡌⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠈⡏⠏⣸⡙⡝⠝⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡗⣀⣤⣀⠺⠿⢇⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠁⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠛⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⣿⣻⣯⣤⣚⢿⣷⠄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣾⣶⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣯⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣯⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠾⠿⢿⣿⣿⣛⢛⣺⣿⣯⣭⣭⡅⣠⢩⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠁⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡷⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⣉⣋⣻⣯⣿⣧⣶⡞⠑⣿⣿⣿⣿⣮⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⠋⠵⢾⣿⣿⣿⡿⠁⠀⠀⣴⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠀⠀⠉⠉⠉⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⡶⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡹⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⣿⣿⣿⡇⢀⡤⣨⡙⣋⣄⣤⣤⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣯⣤⣚⢿⣷⡀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣶⣾⣿⡾⣿⢫⣿⣿⢻⣿⣿⣷⣻⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣧⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣯⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠾⠿⢿⣿⣿⣛⢛⣺⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠁⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡷⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⢉⡉⣉⣉⣉⣿⣯⣧⣶⡞⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⢟⣛⢿⣶⣶⣿⣿⣿⡿⠿⣟⢋⠵⢾⣿⣿⣿⡿⠁⠀⠀⢤⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣱⣿⣿⠃⠁⠀⠉⠉⠉⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢼⣿⣆⡶⣰⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡏⢎⣤⡹⠙⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⠠⣈⡙⡋⣤⣤⣤⣴⣤⣶⣶⣶⣶⣶⣴⣴⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠉⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠲⣶⣿⣿⣿⣿⣿⣿⡟⠒⠒⣤⣀⠀⠀⠀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠴⠶⣿⣿⣿⣿⣿⣿⢿⣛⣛⣲⢾⣿⣷⣄⠀⠀⠀⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣫⠾⣿⣿⣷⣯⢻⣿⣟⣵⣿⣿⣿⣿⣷⡝⣿⣿⣷⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢳⣿⣤⣾⣿⣿⣿⡇⣿⢸⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⠗⣠⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣏⢿⣿⣿⣿⣿⡿⣳⣿⣯⢿⣿⣿⣿⣿⡿⣣⣿⣿⣁⣠⡍⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣭⡟⣛⠽⡄⠤⢴⣖⣦⣌⢭⣭⣽⣾⣿⣿⣿⣿⣿⡇⣤⣦⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡟⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣦⣭⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⣉⣛⣻⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⡇⣿⣿⣿⢳⣇⢿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣍⡻⢏⠾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⡿⣧⣿⢻⣿⣿⣿⣿⣿⣿⣿⡽⠿⢇⣿⣟⠿⣿⣯⣾⡆⠀⠀⠀⠀⠈⠀⠀⠀⣶⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⣿⣿⣿⣿⣾⣷⣿⣟⡿⢫⣯⣝⢻⣿⠟⣶⣶⡝⢟⣣⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⠟⠿⠁⠘⠿⡟⢅⣶⣶⠘⠿⣿⡼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢪⢯⠏⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⢱⣾⣿⣷⣔⣻⡟⠁⢠⣄⣀⣤⣤⣤⣤⣴⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠈⣿⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠉⠁⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⢻⣿⣿⣿⣿⣿⣿⣟⠉⠑⢲⣤⡀⠀⠀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡷⢶⣿⡿⣿⣿⣿⣿⣿⢟⣻⣿⣗⡻⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣫⠾⢿⣿⣿⣷⡽⣿⡟⣽⣿⣿⣿⡿⢿⣮⢿⣿⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⣦⣾⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣦⣴⣿⢸⣿⣿⠟⣠⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡻⣿⣿⣿⣿⡿⣣⠿⢷⡻⣿⣿⣿⣿⡿⣫⣿⣿⣁⣠⡍⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⡭⣩⣱⠶⢰⣖⣻⣥⣦⡻⣿⣷⣾⣿⣿⣿⢿⣿⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡟⡟⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣮⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⣉⣉⣽⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⣿⣺⣿⣿⣿⣿⡇⣿⣿⣿⣿⣮⣝⢋⠸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣿⣿⣿⢻⣾⢻⣿⣿⣿⣿⣿⣿⣿⣏⣻⣟⣾⣯⡛⠿⣫⣾⡄⠀⠀⠀⠈⠈⠀⠀⠀⣦⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣿⣿⣿⣷⣶⣿⣿⡻⢟⣿⡻⣻⣿⡟⣭⣯⡻⣟⣯⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⢯⡻⠃⠘⢿⡿⣊⣭⣤⠹⢿⣷⡹⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠁⢜⣟⡟⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⢿⡿⠂⠀⠀⢪⣼⣶⣦⡠⢾⡿⢃⣠⣄⣀⣤⣤⣤⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠼⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⢻⣿⣿⣿⣿⣿⣿⣟⠉⠑⢲⣤⡀⠀⠀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⢶⣿⡿⣿⣿⣿⣿⣿⢟⣻⣿⣗⡻⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣫⠾⢿⣿⣿⣷⡽⣿⡟⣽⣿⣿⣿⡿⢿⣮⢿⣿⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⠰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⣦⣾⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣦⣼⣿⢸⣿⣿⠟⣠⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡻⣿⣿⣿⣿⡿⣣⠿⠷⡻⣿⣿⣿⣿⡿⣫⣿⣿⣁⣠⡍⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢑⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⡭⣩⣱⠶⢰⣖⣻⣥⣦⡻⣿⣷⣾⣿⣿⣿⢿⣿⡇⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡟⡟⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣦⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⣉⣉⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⣿⣺⣿⣿⣿⣿⡇⣿⣿⣿⣿⣮⣝⢋⠸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣿⣿⣿⢻⣾⢻⣿⣿⣿⣿⣿⣿⣿⣏⣻⣟⣾⣯⡛⠿⣫⣾⡄⠀⠀⠀⠀⠘⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣿⣿⣿⣷⣶⣿⣿⡻⢟⣿⡻⣻⣿⡟⣭⣯⡻⣟⣯⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⢯⡻⠃⠘⢿⠿⣋⣭⣤⠹⢿⣷⡹⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠁⢜⣟⡟⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠂⠀⠀⢺⣼⣶⣦⡠⢾⡿⢃⣀⣤⣄⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⢻⣿⣿⣿⣿⣿⣿⣟⠉⠑⢲⣤⡀⠀⠀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⢶⣿⡿⣿⣿⣿⣿⣿⢟⣻⣿⣗⡻⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣫⠾⢿⣿⣿⣷⡽⣿⡟⣽⣿⣿⣿⡿⢿⣮⢿⣿⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⠰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⣦⣾⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣦⣼⣿⢸⣿⣿⠟⣠⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡻⣿⣿⣿⣿⡿⣣⠿⠷⡻⣿⣿⣿⣿⡿⣫⣿⣿⣁⣠⡍⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⡭⣩⣱⠶⢰⣖⣻⣥⣦⡻⣿⣷⣾⣿⣿⣿⢿⣿⡇⣤⣤⣶⣶⣶⣶⣶⣾⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⡟⡟⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣮⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⣉⣋⣽⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⣿⣺⣿⣿⣿⣿⡇⣿⣿⣿⣿⣮⣝⢋⠸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣿⣿⣿⢻⣾⢻⣿⣿⣿⣿⣿⣿⣿⣏⣻⣟⣾⣯⡛⠿⣫⣾⡀⠀⠀⠀⠀⠘⠀⠀⠀⣦⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣿⣿⣿⣷⣶⣿⣿⡻⢟⣿⡻⣻⣿⡟⣭⣯⡻⣟⣭⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⢯⡻⠃⠘⢿⠿⣋⣭⣤⠹⢿⣷⡹⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠁⢜⣟⡟⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠂⠀⠀⢪⣼⣶⣦⡠⢾⡿⢃⣀⣄⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⢻⣿⣿⣿⣿⣿⣿⣟⠉⠑⢲⣤⡀⠀⠀⠀⠀⠀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⢶⣿⡿⣿⣿⣿⣿⣿⢟⣻⣿⣗⡻⣿⣿⣷⡀⠀⠀⠀⠀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣫⠾⢿⣿⣿⣷⡽⣿⡟⣽⣿⣿⣿⡿⢿⣮⢿⣿⣿⣆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⠰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⣦⣾⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣦⣼⣿⢸⣿⣿⠟⣠⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡻⣿⣿⣿⣿⡿⣣⠿⢷⡻⣿⣿⣿⣿⡿⣫⣿⣿⣁⣠⡍⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⡭⣩⣱⠶⢰⣖⣻⣥⣦⡹⣯⣷⣾⣿⣿⣿⢿⣿⡇⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⡟⡟⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⣮⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⢉⡉⣉⣉⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⣿⣺⣿⣿⣿⣿⡇⣿⣿⣿⣿⣮⣝⢋⠸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣿⣿⣿⢻⣾⢻⣿⣿⣿⣿⣿⣿⣿⣏⣻⣟⣾⣯⡛⠿⣫⣾⡀⠀⠀⠀⠀⠙⠀⠀⠀⣤⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣿⣿⣿⣷⣶⣿⣿⡻⢟⣿⡻⣻⣿⡟⣭⣯⡻⣟⣭⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⢯⡻⠃⠘⢿⡿⣋⣭⣤⠹⢿⣷⡹⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠉⢜⣟⡟⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⢿⡿⠂⠀⠀⢪⣼⣶⣦⡠⢾⡿⢃⣀⣠⣄⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠈⠁⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣶⣾⣿⣼⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⣄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣷⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣯⣽⢲⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢿⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠁⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⢿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢢⡄⠈⠉⡉⢉⣋⣉⣿⣽⣧⣶⡞⠑⣿⣿⣿⣿⣮⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣟⣻⣟⠋⠵⣾⣿⣿⣿⡿⠁⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣿⠋⠁⠀⠀⠉⣉⡈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⠖⣼⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡋⢎⣤⣚⡊⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⣀⣉⡙⣉⣤⣤⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣶⣾⣿⣼⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣷⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣯⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢿⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⣿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡧⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⠉⡉⢉⣋⣉⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣮⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣟⣻⣟⢋⠵⣾⣿⣿⣿⡿⠁⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣽⣿⠋⠉⠀⠀⠉⣉⡈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⠖⣼⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡋⢎⣤⣚⡊⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⣀⣍⡙⣉⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠉⠉⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢷⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⢶⣶⣶⡖⠀⠀⢀⡀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠛⠋⣩⣾⣿⢿⣻⣯⣴⣚⢿⣷⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣯⣶⣶⣾⣿⣼⣿⢫⣿⣿⢻⣿⣿⣷⣹⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⡟⣸⣿⣿⢻⣿⣸⣿⣿⡌⢿⣿⣿⢻⣿⡄⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⡿⣿⠴⠿⠛⠵⣿⣿⣷⡝⡿⠿⠾⢟⣷⣿⠿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢘⣛⡓⣒⣾⣯⣽⢰⣿⣿⣿⣿⣮⠛⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⡾⠿⢿⣿⣿⣛⢛⣾⣿⣯⣭⣭⡅⣠⢭⣤⣤⣀⢶⡆⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⣿⣿⣞⣿⣿⣿⡽⣿⡿⠿⣯⣛⣛⣿⣭⣷⣿⣷⣿⣿⠿⣿⡷⠰⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣮⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡌⣱⣧⢻⣿⣿⣿⣿⣿⣿⡇⢢⡄⠈⠉⡉⢉⣛⣻⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣹⣿⣿⣿⣿⣿⣿⡎⣫⣾⣿⣿⡼⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣟⣻⣟⢋⠵⣾⣿⣿⣿⡿⠁⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣽⣿⠋⠉⠀⠀⠉⣉⡈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⢾⣿⣆⠖⣼⣿⡇⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢈⡋⢎⣤⣚⡊⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⢸⣿⣿⣿⣿⡇⠀⣀⣉⣉⣉⣤⣴⣤⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⣴⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣏⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣀⢤⣾⡄⠘⠛⠀⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣫⣾⣿⣃⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢯⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⠾⣙⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠟⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣾⣿⣷⢶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡧⣦⡄⠉⣉⡉⣉⣻⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⠟⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡶⠍⢛⣯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⠀⠂⢀⠈⠙⠃⢰⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡥⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⡣⢧⣹⡝⡝⡽⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⡖⣠⣀⣀⠾⠿⢏⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠉⠉⠀⠉⠁⠈⠉⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⡛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣻⣾⣿⣇⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣙⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠋⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⡭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⠠⢽⣛⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣶⣶⣤⣹⣿⣷⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣷⣦⡄⠉⡉⠉⣉⣉⣉⣉⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⢟⣥⣾⣿⣿⡀⠙⠿⣿⠿⠋⢠⣿⠉⢿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠝⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣧⣀⠙⠛⠛⠛⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⢐⠢⡒⢌⡙⠋⢸⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡭⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠁⠀⡣⢧⣹⡟⡝⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⡖⣠⣄⣄⠾⠿⢏⣴⣶⣶⣶⣶⣶⣿⣿⣷⣶⣿⣿⣿⣶⣭⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠉⠉⠙⠁⠉⠉⠉⠉⠉⠉⠉⠉⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠛⠾⠿⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣽⣿⣿⣿⣿⡿⠿⠿⢃⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⢶⣶⠶⠒⠤⢄⡀⠀⣾⣿⣿⣏⡼⠣⢢⢏⣽⢻⢿⣷⣧⣏⠎⣼⢘⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣯⣷⣶⣶⣤⣄⢤⣾⡄⠘⠛⠂⣿⣿⣿⠛⢿⣷⣦⣸⢡⢰⢏⡝⡻⣿⣿⣧⣿⡟⡴⡕⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣯⣿⣫⣾⣿⣇⢹⣿⡏⣼⢃⠎⡝⢿⣿⣦⣎⡄⡰⢡⢦⣿⠿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣽⣶⣶⣶⣶⣿⣽⡻⢧⣿⠹⠿⠻⣿⣄⢻⣿⣷⣦⡞⢤⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣺⢾⣙⠾⠎⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠋⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠛⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⠭⣠⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣈⢎⠘⣹⠹⣻⣿⣿⣿⣿⠟⠠⢭⣛⡿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⣿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣶⣶⣤⣹⣿⣷⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣷⣦⡄⠉⡉⠉⣉⣉⣉⣉⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡣⣾⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠱⠿⠿⠿⠿⠿⢟⣡⣶⣿⣿⡀⠙⠿⣿⠿⠋⢠⣿⠉⢿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡶⠝⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣧⣀⠙⠛⠛⠛⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⢐⠢⣒⠈⡝⠋⢸⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡭⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠁⠀⡫⢧⣹⡝⡽⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣿⣿⡖⣠⣤⣀⠾⠿⢏⣴⣶⣶⣶⣶⣶⣾⣿⣷⣾⣿⣿⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠉⠉⠛⠁⠉⠁⠉⠉⠉⠉⠉⠁⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠛⠾⠯⢿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠒⠺⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠠⣶⣶⣶⣤⣤⣤⣀⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢟⣲⣖⣒⢿⣿⣿⣿⣿⣿⣅⣀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣵⣿⣿⣿⣿⣷⡽⣿⣿⣫⣶⣿⣿⣆⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣿⣿⡿⢿⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⡿⣳⠿⠏⢿⣿⣿⣭⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣮⣽⣯⣽⡾⣵⡶⠭⣶⢙⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣾⣷⢩⣀⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⠠⢭⣒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣴⣶⣤⣹⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⡇⣦⡄⠉⠉⠉⣉⣉⣉⣉⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣮⣛⢵⣿⣿⣿⣿⣿⣿⣿⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠣⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⡀⠙⠿⣿⠿⠋⢠⣿⠀⢻⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣍⣭⡝⢿⡟⣿⣮⣛⣵⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⣴⣦⡆⠀⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣧⣀⠙⠛⠛⠛⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⣸⣿⡇⠀⠉⠙⠻⠿⠟⠃⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⣿⣸⣷⣤⣄⣀⣀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⢠⠀⠀⠀⢠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢷⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠠⣴⣶⣶⣦⣤⣤⣀⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢟⣲⣖⣒⢿⣿⣿⣿⣿⣿⣅⣀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣵⣿⣿⣿⣿⣷⡽⣿⣿⣫⣶⣿⣿⣦⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣿⣿⡿⢿⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡻⣿⣿⣿⣿⡿⣳⠿⠏⢿⣿⣿⣭⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣮⣽⣯⣽⡾⣵⡶⠭⣶⢛⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣾⣷⢩⣀⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⣠⣬⣒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣦⣤⣉⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⢿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⡇⣢⡄⠉⠉⠉⣉⣉⣉⣉⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣮⣛⢵⣿⣿⣿⣿⣿⣿⣿⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠫⠿⠿⠿⠿⠿⠇⣠⣶⣿⣧⠀⠻⢿⣿⠿⠋⢀⣿⠉⢻⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣍⣭⡝⢿⡟⣿⣮⣛⣵⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣿⣿⣷⣄⠉⠛⠛⠛⠋⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⣸⣿⡇⠀⠉⠙⠻⠿⠟⠃⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣸⣷⣤⣄⣀⣀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⣀⠀⠀⠀⢠⣴⣤⣶⣴⣴⣶⣶⣶⣶⣶⣶⣾⣿⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠠⣴⣶⣶⣦⣤⣤⣀⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢟⣲⣖⣒⢿⣿⣿⣿⣿⣿⣅⣀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣵⣿⣿⣿⣿⣷⡽⣿⣿⣫⣶⣿⣿⣆⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣿⣿⡿⢿⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⡿⣳⠿⠏⢿⣿⣿⣭⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣮⣽⣯⣽⣾⣽⡷⡰⣶⢛⠛⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⣡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣷⢩⣀⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⣀⠉⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣿⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣧⢢⡄⠉⠉⡉⢉⣙⣻⣿⣿⣧⣶⡟⠙⣿⣿⣿⣿⣮⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣮⣛⢵⣿⣿⣿⣿⣿⣿⣿⣷⣶⡁⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠫⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣍⣭⡝⢿⡿⢿⣟⠿⣹⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣛⣿⣿⣿⣞⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⣸⣿⡇⠀⠉⠸⢿⣿⡿⠁⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣯⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣸⣷⣤⣄⣀⣀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⣤⠀⠀⠀⢠⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢷⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⢏⢝⢛⢿⣿⣿⣿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⣿⡉⠉⣁⣽⣍⠙⠛⢻⣿⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⣶⣿⢿⣿⣶⣭⣻⣿⢟⣯⣭⣭⣭⣽⣀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣻⡻⣿⣿⣿⣿⣿⣿⢇⣏⣿⣿⣿⣿⣽⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣭⣵⣶⡢⣶⣤⢠⠤⢶⠮⠛⣛⠟⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡜⣋⣛⣏⣭⣼⣷⣁⣠⣭⣤⣤⣤⣶⣶⣶⡄⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢳⣾⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣿⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢉⣿⣿⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⢉⣛⣹⣿⣿⣧⣶⡟⠙⣿⣿⣿⣿⣮⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡙⢣⠿⠿⠿⠿⠿⠿⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣟⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢙⣫⣾⠈⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣛⣿⣿⣿⣞⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠈⠉⠛⠻⠿⠿⠩⣭⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣯⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⣿⣸⣷⣤⣄⣀⣀⠀⠀⣮⣟⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⣠⠀⠀⠀⢠⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⡀⢸⣿⣿⠟⠋⠀⠀⠀⠁⠀⠀⠀⠈⠀⠉⠁⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢷⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⢏⢝⢛⢿⣿⣿⣿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡉⠉⣁⣽⣍⠙⠛⢻⣿⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⣶⣿⢿⣿⣶⣭⣻⣿⢟⣯⣭⣭⣭⣽⣀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣻⡻⣿⣿⣿⣿⣿⣿⢧⣏⣿⣿⣿⣿⣽⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣭⣵⣶⡢⣶⣤⢠⠴⢶⠮⠛⣻⠟⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡜⣋⣛⣏⣭⣼⣷⣁⣠⣭⣤⣤⣤⣶⣶⣶⡄⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢛⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢳⣷⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢉⣿⣿⣿⣿⣿⣿⡧⢢⡄⠉⢉⡉⣉⣋⣹⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡙⢣⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣟⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢙⣫⡾⠈⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠈⠉⠛⠻⠿⠿⠩⣭⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⣿⣸⣷⣤⣄⣀⣀⠀⠀⣮⣟⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⣠⠀⠀⠀⢠⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠁⠀⠀⠀⠉⠀⠉⠁⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢷⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⢏⢝⢟⢿⣿⣿⣿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡉⠉⣁⣽⣍⠙⠛⢻⣿⣇⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⣶⣿⢿⣿⣶⣭⣻⣿⢟⣯⣭⣭⣭⣽⣀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣻⡻⣿⣿⣿⣿⣿⣿⢇⣟⣿⣿⣿⣿⣽⡿⢋⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⠰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣭⣵⣶⢢⣾⣤⢠⡤⠶⠮⠛⣻⠟⣡⣶⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣜⡧⣩⣍⣵⣾⣷⣁⣠⣭⣤⣤⣤⣶⣶⣶⡄⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢳⣾⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢉⣿⣿⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⢉⣋⣻⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡙⢣⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣟⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣙⣫⣾⠈⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣟⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠈⠉⠛⠻⠿⠿⠩⣭⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣿⣿⣸⣷⣤⣄⣀⣀⠀⠀⣮⣛⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⠇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⣠⠀⠀⠀⢠⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠈⠀⠀⠀⠀⠉⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⢶⣶⣶⣶⣶⣦⣤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣽⣿⣶⣤⣀⡀⣤⣿⠈⠸⠿⢿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣽⣿⡷⣠⣤⣼⣅⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣽⣿⣿⡻⣿⣿⡿⣹⣿⢼⣿⣿⣷⣾⡆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡑⣻⢦⡜⣈⣙⣫⣽⡶⢊⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⣝⢖⢿⣩⠕⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⣮⣁⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⣉⣙⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣦⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⠀⠠⠀⠍⠙⠃⢰⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⡃⢧⣸⡝⡽⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡶⢀⣄⣄⠾⠿⢏⣴⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⢶⣶⣶⣶⣶⣦⣤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣽⣷⣶⣤⣀⡀⣤⣿⠈⠸⠿⢿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣽⣿⡷⣠⣤⣼⣅⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣽⣿⣿⡻⣿⣿⡿⣹⣿⢼⣿⣿⣷⣾⡆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡑⣻⢦⡜⣈⣙⣫⣽⡶⢊⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⣝⢗⠿⣩⠕⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⣮⣁⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⣼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⢉⣋⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⠀⠀⠀⠉⠙⠃⢰⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⡃⢧⣸⡟⡽⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡶⢀⣄⣄⠾⠿⢏⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠈⠀⠈⠉⠀⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠾⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⢶⣶⣶⣶⣶⣶⣤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢛⣽⣷⣶⣤⣀⡀⣤⣿⠈⠸⠿⢿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣿⣷⣿⣿⣿⣿⣿⣽⣿⡷⣠⣤⣼⣅⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣽⣿⣿⡻⣿⣿⡿⣹⣿⢼⣿⣿⣷⣾⡆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⡑⡶⢦⡈⣈⣛⢫⣽⡶⢊⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣽⢒⠯⣩⠕⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣥⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣸⢯⣁⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⣉⣙⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣦⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⠀⠀⠀⠍⠙⠃⢰⣾⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⡃⢧⣸⡟⡽⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡶⢀⣄⣀⠾⠿⢏⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠈⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⢶⣶⣶⣶⣶⣦⣤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⢟⣽⣿⣶⣤⣀⡀⣤⣿⠈⠸⠿⢿⡆⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡝⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡧⣿⣷⣿⣿⣿⣿⣿⣽⣿⡷⣠⣤⣼⣅⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣽⣿⣿⡻⣿⣿⡿⣹⣿⢼⣿⣿⣷⣾⡆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢃⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡑⣻⢦⡄⣈⣙⣫⣽⡶⢊⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡍⣝⢒⠿⣩⠕⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⣮⣁⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢾⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⣉⣫⣹⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣿⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⠀⠀⠀⠍⠙⠃⢰⣾⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⡃⢧⣸⡟⡽⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡶⢀⣤⣀⠾⠿⢏⣴⣶⣶⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠁⠈⠉⠀⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠿⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⢶⣶⣶⣶⣶⣦⣤⣄⡀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢟⣽⣷⣶⣤⣀⡀⣤⣿⠈⠸⠿⢿⡄⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡧⣿⣷⣿⣿⣿⣿⣿⣽⣿⡷⣠⣤⣼⣅⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣽⣿⣿⡻⣿⣿⡿⣹⣿⢼⣿⣿⣷⣾⡆⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡑⣻⢦⡔⣈⣙⣫⣽⡶⢊⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⢟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡍⣝⢒⠿⣩⠕⣡⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣵⣡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⣡⣿⣿⣿⡇⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⢸⣮⣁⣠⣭⣤⣤⣤⣶⣶⣶⣤⡙⠻⣿⣿⣿⣿⣿⣷⣿⣧⣀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠇⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⢼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⡧⣢⡄⠉⢉⡉⣉⣋⣿⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣝⡡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠱⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡾⠍⢛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣶⣶⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣻⣻⣿⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⣾⣿⠟⠀⠀⠀⠉⠙⠃⢰⣾⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣿⠛⠁⢸⣿⣷⢲⡤⣴⣶⡆⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⡣⢧⣸⡟⡽⡿⠁⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⡶⢠⣄⣀⠾⠿⢏⣴⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠿⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⢤⠤⢿⣿⣿⣿⣿⣿⣿⡏⠁⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣵⣿⣿⣿⣿⣎⢿⣿⡿⣫⣿⣶⣿⣕⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⢼⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⡻⣿⣿⣿⣷⢞⣼⣧⢿⣿⣿⣿⣿⣍⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢻⣿⣶⣬⡜⠰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠪⣿⣦⢠⣤⠴⠿⢅⡛⠿⠿⢿⣻⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⣾⣿⣞⠿⡻⠿⠹⠿⣸⣿⣮⡻⣿⣿⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⠀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣷⣶⣶⣮⢻⣿⣿⣿⣿⡟⢠⣴⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⣿⢿⡸⣿⣿⡟⣵⣶⣴⣶⣬⣶⡆⣿⣿⣿⣿⣿⢯⣿⣿⣿⡶⣼⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⢉⣋⣹⣟⣭⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣛⣲⣶⣶⣶⣶⣶⣶⣶⣾⣷⣭⣭⣽⣯⡭⢞⣵⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣷⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣚⡿⢿⣿⡏⠈⠈⠀⠀⠀⣤⣴⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣻⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣎⠿⠿⠿⠛⠛⠁⣾⣿⡿⠿⠿⢿⣿⣷⣯⠀⠀⠀⠀⠀⠀⠛⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢚⣿⠿⠛⠗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣄⢀⣀⠀⠚⣛⡛⠯⠭⢂⣶⣶⣶⣶⣴⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠳⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⢤⡤⢿⣿⣿⣿⣿⣿⣿⡏⠁⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣵⣿⣿⣿⣷⣎⢿⣿⡿⣫⣿⣶⣿⣕⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⢼⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⡻⣿⣿⣿⣷⢞⣼⣧⢿⣿⣿⣿⣿⣍⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢻⣿⣶⣬⡜⠰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠪⣷⣦⢠⣤⠴⠿⢅⡛⠿⠿⢿⣻⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⣼⣿⣞⠿⡻⠿⠹⠿⣸⣿⣮⡻⣿⣿⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⠀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣷⣶⣶⣮⢻⣿⣿⣿⣿⡟⢠⣴⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣁⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⣿⢿⡸⣿⣿⡟⣵⣶⣴⣶⣬⣶⡆⣿⣿⣿⣿⣿⢯⣿⣿⣿⡶⣽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢢⡄⠉⢉⡉⢉⣉⣙⣿⣯⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣛⣲⣶⣶⣶⣶⣶⣶⣶⣾⣷⣭⣭⣿⣯⡭⢞⣵⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣚⡿⢿⣿⡏⠈⠁⠀⠀⠀⣴⣴⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣎⠿⠿⠿⠛⠛⠁⣾⣿⡿⠿⠿⢿⣿⣷⣯⠀⠀⠀⠀⠀⠀⠛⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣧⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣿⠿⠛⠗⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣄⣀⣀⠀⠚⣛⡛⠯⠭⢂⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠋⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠲⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣽⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⢼⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣷⢞⣼⣇⢿⣿⣿⣿⣿⣉⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣷⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣟⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣮⢻⣏⢺⡿⣷⡭⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⠀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡄⠉⢉⡉⢉⣋⣙⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠀⠀⠀⠀⣴⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣽⣟⠭⠾⠿⠛⠛⠁⣾⣿⣿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⢀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢉⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⢼⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣷⢞⣼⣇⢿⣿⣿⣿⣿⣉⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣷⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣟⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣮⢻⣟⢺⡿⣷⡭⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣴⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⡄⠉⢉⡉⢉⣛⣟⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠀⠐⠀⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣽⣟⠭⠾⠿⠛⠛⠁⣾⣿⡿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣶⣦⣶⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠯⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⢸⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣷⢞⣼⣇⢿⣿⣿⣿⣿⣉⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣛⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣮⢻⣟⢺⡿⣷⡭⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⢉⡉⢉⣙⣫⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡟⠈⠀⠀⠀⠀⣴⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣿⣟⠭⠾⠿⠛⠛⠁⣾⣿⣿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣦⣶⣶⣾⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⢤⡤⢿⣿⣿⣿⣿⣿⣿⡟⠁⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣵⣿⣿⣿⣿⣏⢿⣿⡿⣫⣿⣶⣿⣕⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⢿⢼⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⡻⣿⣿⣿⣷⢞⣼⣧⢿⣿⣿⣿⣿⣍⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠪⣿⣦⢠⣤⠴⠿⢍⡛⠿⠿⢿⣫⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⣾⣿⣜⠿⡻⠿⠹⠿⣸⣿⣮⡻⣿⣿⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣷⣶⣶⣮⢻⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⢿⡸⣿⣿⡟⣵⣶⣴⣶⣮⣶⡆⣿⣿⣿⣿⣿⢯⣿⣿⣿⡶⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡄⠉⢉⡉⢉⣉⣍⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣛⣲⣶⣶⣶⣶⣶⣶⣶⣾⣷⣭⣭⣿⣯⣭⢞⣵⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠀⠀⠀⠀⣴⣴⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣻⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣎⠿⠿⠿⠛⠛⠁⣾⣿⡿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣦⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣹⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣼⣿⣿⣿⣿⣿⢼⡟⢘⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣿⢟⣼⣧⢿⣿⣿⣿⣿⣿⡿⣼⣿⡿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⣡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣟⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣮⢻⡟⢺⡿⣷⡭⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⠀⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣴⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢠⡄⠉⢉⡉⢉⣋⣩⣿⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠁⠀⠀⠀⣴⣦⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣟⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣿⣟⠭⠾⠿⠛⠛⠁⣾⣿⡿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣦⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠶⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠑⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣹⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣼⣿⣿⣿⣿⣿⢼⡟⢘⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣿⢟⣼⣇⢿⣿⣿⣿⣿⣿⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣟⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⢻⡟⢺⡿⣷⡩⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣠⡄⠉⢉⡉⢉⣙⣹⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠀⠀⠀⠀⣴⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣿⣟⠭⠾⠿⠛⠛⠁⣾⣿⣿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⡀⣀⡀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣶⣦⣶⣶⣷⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠈⠀⠉⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣹⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣼⣿⣿⣿⣿⣿⢼⡟⢘⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⢻⣿⣿⣿⣿⢟⣼⣧⢿⣿⣿⣿⣿⣿⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣟⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⢻⡟⢺⡿⣷⡩⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⢉⡉⢉⣙⣹⣟⣿⣧⣶⡞⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠀⠁⠀⠀⠀⣴⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣿⣟⠭⠾⠿⠛⠛⠁⣾⣿⡿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⡀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣦⣶⣶⣶⣶⣶⣶⣭⣛⣛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠯⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣹⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣼⣿⣿⣿⣿⣿⢼⡟⢘⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣿⢟⣼⣧⢿⣿⣿⣿⣿⣿⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢻⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣟⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⢻⡟⢺⡿⣷⡩⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡈⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⠀⠉⢂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣤⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡄⠉⢉⡉⢉⣋⣫⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠗⣡⣶⣿⣿⣻⣿⣿⣿⣿⣿⣏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠀⠀⠀⠀⣤⣦⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣟⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣿⣟⠭⠾⠿⠛⠛⠁⣾⣿⡿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠙⠛⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣭⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣶⣦⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⢤⠤⢿⣿⣿⣿⣿⣿⣿⡟⠁⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡰⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣵⣿⣿⣿⣷⣎⢿⣿⡿⣫⣿⣶⣿⣕⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣼⣿⣿⣿⣿⣿⢼⡟⣘⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⡻⣿⣿⣿⣿⢟⣼⣧⢿⣿⣿⣿⣿⣿⡿⣼⣿⡿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠟⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠪⣿⣦⢠⣤⡴⠿⢍⡛⠿⠿⢿⣫⣾⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣫⣾⣿⣜⠿⡻⠿⡹⠿⣸⣿⣮⡻⣿⣿⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣷⣶⣶⣮⢻⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⠴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⢿⡸⣿⣿⡟⣵⣶⣴⣶⣮⣶⡆⣿⣿⣿⣿⣿⢯⣿⣿⣿⡶⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⡄⠉⢉⡉⢉⣉⣩⣟⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣛⣲⣶⣶⣶⣶⣶⣶⣶⣾⣷⣭⣭⣿⣯⡭⢞⣵⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣡⣶⣿⣿⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠈⠀⠀⠀⣤⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣎⠿⠿⠿⠛⠛⠁⣾⣿⣿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣶⣤⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⢸⣿⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠸⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣳⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⠿⢸⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣿⢞⣼⣇⢿⣿⣿⣿⣿⣋⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣛⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⡠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣮⢻⣟⢺⡿⣷⡩⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⠀⠈⢂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣦⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⡴⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⢉⡉⢉⣉⣋⣿⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⣻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠀⠀⠀⠀⣤⣤⡄⠀⣾⣿⣿⣿⣿⣷⣽⣛⣟⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣽⣟⠭⠾⠿⠛⠛⠁⣾⣿⣿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠛⠛⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢀⡀⢀⣀⣀⠾⢟⠻⠯⠗⢂⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠾⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣻⠿⣿⣿⣿⣿⡿⢁⢊⠟⡻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⡼⠣⢢⠏⡽⢻⢿⣷⣧⣎⠎⣼⢐⣽⡟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡁⠠⠤⢿⣿⣿⣿⣿⣿⣿⡟⠓⠂⢄⡀⠀⠀⣿⣿⣿⠛⢿⣷⣦⣸⢁⢰⢎⡜⡻⣿⣿⣧⣾⡟⡴⡅⣬⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣳⣾⣿⣿⣷⣝⢿⣿⡿⣫⣽⣿⣯⣖⢿⣿⣦⡀⢹⣿⡏⣼⠃⠎⡝⢿⣿⣦⣎⡄⡰⠡⢦⣿⠿⢿⣷⣵⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⠿⢸⡟⣾⣿⣿⣿⣿⣿⣧⢿⣿⣷⡀⢻⣿⣷⣦⡞⢠⣿⢋⠍⡿⢿⣷⣧⣿⢁⢢⠏⠌⡿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣯⢻⣿⣿⣿⣿⢞⣼⣇⢿⣿⣿⣿⣿⣋⡿⣼⣿⠿⢃⣴⣿⣿⣿⣿⣿⣧⣊⡝⡔⡰⠉⠝⢿⣿⣶⣬⡜⡰⢡⢃⠟⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣿⣿⣮⡭⠧⢒⣪⣽⣿⣮⣻⠿⣿⠿⣛⣽⠟⣡⣴⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣾⣥⡡⣠⢃⣂⠟⢻⣿⣿⣧⣂⡾⢡⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⢻⡟⢺⡿⣷⡩⣾⣿⣿⣿⠿⠿⠿⣟⣁⣠⣭⣤⣤⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣿⣧⡀⠎⠘⣹⠹⣻⣿⣿⣿⣿⠟⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣵⣿⣿⣿⣿⣿⣿⢸⢸⣷⣾⣶⡆⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣤⣉⠛⠿⢿⣿⣿⣿⣿⣾⣼⣃⣾⣿⣿⡿⠟⣡⡼⣿⣷⢶⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣢⡄⠉⢉⡉⢉⣉⣏⣟⣿⣧⣶⡟⠑⣿⣿⣿⣿⣯⢽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣘⣭⣝⣭⣱⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣎⣾⣿⣿⢹⣿⠿⠿⠿⠿⠿⠿⠿⠇⣠⣶⣿⣿⢻⣿⣿⣿⣿⣿⢏⣿⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⣷⣯⣭⣷⡿⣿⣿⣿⣿⡿⢿⣛⣛⣀⣺⠿⣿⣿⡏⠈⠂⠀⠀⠀⣤⣤⡆⠀⣾⣿⣿⣿⣿⣷⣽⣛⣛⣛⣽⣿⣿⣞⢿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣮⣽⣟⠭⠾⠿⠛⠛⠁⣾⣿⣿⠿⠿⣿⣿⣷⣍⠀⠀⠀⠀⠀⠀⠙⠙⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣭⣽⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣀⣤⣶⣇⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢝⣛⡿⠿⠷⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣄⡀⣀⠾⢟⠻⠯⠗⢂⣶⣴⣶⣶⣶⣶⣶⣶⣶⣭⣛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣟⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠀⠀⠀⢸⣿⣿⠟⠉⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠺⠏⠿⢟⣿⢿⣯⣭⢍⣥⣬⣿⣿⣮⠻⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⢽⣿⣿⣿⣿⡿⠿⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠖⠺⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3256

╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕

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    Gemini version at gemini://gemini.techrights.org/2023/01/14/unlimited-time-off/

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Gemini_version_available_♊︎


✐ New_Word/Term_for_Microsoft_Layoffs:_Unlimited_Time_Off⠀✐


Posted in Deception, Microsoft at 1:28 am by Dr. Roy Schestowitz


This was posted_hours_ago:


                       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Can_confirm⦈_


Also see: Microsoft_to_offer_unlimited_time_off_for_US_staff


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_is_to_allow_US_staff_to_take_unlimited_time_off_in
a_policy_change_that_is_supposed_to_give_them_more_flexibility_but,
unsurprisingly,_will_also_have_a_cost_benefit_to_Redmond.⦈_


Summary: The_latest_layoffs_seem_to_have_already_begun, but Microsoft does not
call them layoffs


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡙⢿⣿⡇⠀⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⡏⣤⣿⡇⠀⣿⣿⡆⡏⠝⡍⣍⢿⣷⢸⣶⢢⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⡇⠀⣿⣧⣵⣤⣥⣥⣯⣼⣿⣬⣧⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⣇⠸⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣇⡛⣿⣿⣿⣿⣷⢰⠐⠀⡆⢾⡰⡁⣾⡧⡀⣰⣌⡦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣩⢹⣿⡿⠿⢿⡿⠿⡿⠿⢿⣯⢹⠉⣿⠿⢿⡿⠿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠁⢀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣤⠘⣿⣷⢰⣞⢨⣥⣷⢸⡆⣹⢸⡆⡇⢬⡬⢄⡁⣿⣿⢸⢠⡌⡆⡏⣴⢹⠐⢸⢰⣿⡇⣤⠁⠂⠀⣠⠍⣐⣱⢰⡜⡆⣾⣿⢱⡌⡄⣦⣿⣷⢰⡏⣦⢡⢰⠌⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣶⣿⣶⣶⡟⢰⣶⣷⣾⣶⣷⣶⣾⣶⣶⣿⣿⣜⣶⣶⣷⣾⣶⣾⣶⣾⣶⣾⣷⡾⠁⢀⣴⣶⣾⣶⣶⣾⣶⣷⣾⣿⣶⣾⣶⣷⣾⣿⣶⣷⣶⣟⣰⣾⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣺⡟⣊⣿⣿⣿⣿⡿⣫⡹⣻⠛⢿⡿⠻⠻⡿⢻⠉⠹⠻⠟⠻⣿⣿⣿⡟⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣿⣿⣿⣿⣿⣬⣥⣬⣬⣼⣧⣵⣭⣧⣭⣼⣤⣯⣤⣥⣿⣿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⡯⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡆⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢟⣵⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⡿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿
⣧⣤⣬⣤⣾⣼⣤⣴⣤⣵⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣼⣍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠹⠉⡏⢛⣻⢛⢛⢻⠛⡟⡛⡋⡉⣿⢛⢟⡻⣿⢛⢛⢙⠹⠛⡟⣻⡟⡟⡟⡛⢹⢹⠛⠛⡏⡋⡟⠻⢛⢹⡟⡋⡟⡛⡛⠟⢻⡿⢛⠋⠉⣹⡏⡙⡛⡟⣻⡏⡏⣏⠭⢿⡟⢻⢙⠛⢛⢙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣧⣦⣧⣦⣼⣼⣮⣾⣤⣶⣵⣧⣧⣿⣦⣦⣴⣿⣬⣾⣼⣴⣤⣧⣿⣧⣤⣧⣧⣼⣼⣼⣤⣧⣧⣧⣴⣬⣼⣷⣤⣧⣧⣧⣦⣼⣷⣤⣦⣦⣿⣧⣷⣵⣧⣿⣧⣤⣷⣥⣾⣧⣴⣬⣤⣼⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⢿⠿⠿⢿⠻⢿⠿⣿⢿⠿⠿⠿⡿⡿⡿⡿⠿⣿⠿⡿⠟⠻⠿⡿⡿⠿⡿⠿⡿⡟⠿⡿⠿⢿⡿⡿⣿⠿⠿⢿⢿⠿⠿⣿⠿⠿⡿⢻⡿⠿⣿⠿⢿⠿⢿⠿⡿⠻⢿⢿⠿⠿⠿⠟⢻⡿⠿⢿⠟⢿⡿⠿⢿⠟⣿
⣿⣿⣤⣥⣥⣤⣧⣤⣦⣁⣧⣵⣥⣼⣤⣬⣤⣤⣤⣤⣾⣨⣮⣤⣤⣝⣹⣧⣿⣤⣔⣱⣧⣤⣥⣤⣽⣧⣬⣼⣤⣯⣧⣤⣤⣤⣿⣤⣼⣯⣼⣯⣤⣥⣤⣧⣤⣬⣤⣿⣯⣼⣿⣤⣭⣤⣽⣏⣧⣧⣤⣥⣬⣯⣥⣤⣥⣿
⡟⠝⠍⠉⠭⠉⣯⡬⠉⣽⢑⠙⠙⠩⣯⠉⠫⠋⡙⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣥⣥⣤⣤⣤⣥⣤⣬⣤⣼⣤⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣬⣯⣤⣼⣤⣤⣼⣿⣴⣵⣥⣯⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠏⠙⢛⠛⠛⠛⢻⠙⢻⠛⣿⠋⠙⠻⢻⠹⠉⢹⠛⠛⢋⣝⠛⣟⠛⠙⠛⡿⢛⠋⠛⠋⠛⠛⢹⠛⠛⠛⡟⠋⣹⢛⡿⢻⠛⠛⠉⢛⢻⠛⡛⠻⡛⠛⢻⠋⠛⠛⡏⢻⠛⠛⠛⠛⠛⠛⠛⢻⡛⢻⠛⠙⡛⣟⢛⠛⢛
⡿⠿⠿⠿⢿⠛⠿⠿⠻⠛⠿⢿⠻⠿⢿⣿⡿⠿⢿⠿⠿⠿⠟⠿⠿⠿⣿⢿⠛⣿⠟⠿⠿⡿⡿⢿⠿⡿⢿⠿⠿⠿⡟⠿⠿⠾⠟⠻⡷⢿⣟⠿⠿⠻⠾⢿⢿⢿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⣷⣶⣶⣶⣾⣶⣶⣾⣶⣶⣮⣾⣶⣶⣮⣿⣿⣶⣶⣦⣷⣷⣶⣷⣵⣵⣽⣶⣶⣿⣶⣶⣶⣿⣶⣶⣶⣷⣾⣶⣶⣶⣷⣷⣶⣶⣶⣶⣷⣿⣿⣶⣶⣶⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⠿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⣿⣷⣤⣤⣬⣧⣶⣷⣤⣿⣧⣤⣤⣼⣤⣾⣤⣴⣼⣶⣤⣼⣥⣽⣮⣮⣼⣠⣤⣤⣼⣦⣤⣼⣤⣤⣤⣤⣤⣤⣬⣤⣄⣾⣥⣦⣤⣆⣠⣤⣬⣿⣤⣾⣵⣤⣧⣮⣤⣽⣤⣤⣤⣼⣴⣬⣄⣤⣤⣽⣤⣾⣤⣾⣿⣿⣿⣿
⡏⣉⣉⡉⣉⣩⣏⣥⣈⣉⣩⣏⣉⣇⣉⣉⣉⣉⣉⣡⣹⣩⣏⣹⣉⣉⣉⣉⣉⣏⣹⣏⣈⣁⣘⣏⣉⢉⣉⣁⣉⣁⣇⣩⣉⣇⡉⣹⠶⠈⠉⠏⠌⠩⠉⠉⣿⣎⣉⣉⣸⣉⣉⣍⣉⣱⣋⣹⣈⣉⣩⣉⣈⣩⣉⣉⣉⣸
⡟⠛⠛⠋⠛⠛⠋⠛⠛⠛⡟⠛⠛⡟⡛⢟⠛⠋⠛⡛⡟⢛⠋⠛⢛⡟⣻⠛⡟⠛⠛⠛⢻⠉⠛⠛⠙⠙⢻⣛⢛⢛⠛⢻⠛⡛⠛⡟⢻⠛⠛⠻⢛⠛⢻⡛⢛⠛⡟⠛⠛⠛⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢻⡿⣿⠿⠿⢿⠿⠿⠿⣿⠿⠿⠿⢻⣿⠻⠿⡟⠻⠻⠿⠻⠿⠿⢿⠿⠻⠿⠿⡿⢿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠻⢿⠿⡟⠿⡟⠻⣿⠿⢿⢿⠿⠿⠿⠟⡿⣿⢿⢿⠿⠿⢿⠿⠿⠛⡿⢿⠻⠿⡟⣿⠛⠟⠿⠿⠿⠿
⣷⣶⡶⣾⣶⣧⣼⣶⣶⣶⡾⣶⣶⣶⣶⣿⣾⢶⣿⡶⣷⣷⣶⣶⡾⢾⢤⣶⣶⡶⣷⣾⣶⡶⡼⣾⢤⣧⣴⣶⣶⣶⣦⣷⣷⣶⣷⣶⣿⣶⣶⡾⡷⣶⣶⣶⣶⡷⣾⣷⣶⣶⣾⣴⣶⣶⡮⣾⡶⣶⣷⢾⢶⣷⣶⣶⣶⣶
⣧⣤⣤⣬⣦⣤⣼⣤⣤⣄⣤⣤⣡⣤⣤⣬⣧⣦⣤⣤⣤⣴⣤⣦⣤⣼⣤⣤⣇⣠⣵⣤⣾⣧⣬⣧⣤⣄⣦⣯⣤⣧⣤⣤⣠⣤⣤⣤⣤⣷⣤⣤⣤⣤⣰⣬⣧⣤⣤⣤⣀⣤⣤⣤⣧⣤⣤⣷⣦⣤⣤⣼⣤⣥⣦⣤⣽⣿
⣿⣍⣍⡉⣹⣋⣉⣹⣉⣉⣉⣏⣉⣹⢹⣉⣉⣉⢙⣽⣉⣉⣉⡉⣻⡭⣩⡏⣉⣉⣩⡋⣉⣉⣿⣭⡋⣩⣉⣉⣏⣉⡉⣉⣩⣏⣉⢙⢟⢩⡹⣏⣉⣉⣉⢉⣋⢙⣭⡋⣩⣹⣉⣉⣉⡏⢏⡝⣯⣉⣉⣉⡩⡉⣉⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠋⢛⠻⡏⠏⠙⢛⠛⠛⠋⢻⠛⠛⠛⠛⢛⠟⠛⠛⢻⠻⠉⡟⡛⠛⡟⠛⠛⠛⢹⠛⢻⠻⠛⠙⡟⠛⡟⠟⠛⠛⠛⢻⠙⠛⠛⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢻⡿⠿⠿⠿⢿⠿⠛⠻⡿⠿⠿⠿⠿⠟⡟⠿⠟⢿⠻⠿⡿⠿⠟⠻⠿⠿⠿⠿⠟⡿⠿⠛⡿⠿⠿⠿⠿⠿⡿⢿⡿⡿⠿⡿⠿⠿⢿⠿⠿⠿⣿⠿⢿⢻⠻⠿⡟⠻⠻⣿⠿⡿⠻⡿⡟⣿⠻⠛⡿⢿⠿⠿⠛⣿⣿⣿
⣷⣷⣿⡶⣶⣶⣾⣶⣶⡶⣷⣶⣶⣶⣶⣶⣷⣷⣶⣶⡶⣶⣷⣶⣶⢶⣶⡶⣷⣶⣶⣷⡾⢶⣿⣶⣶⢾⣷⣶⣷⣾⣶⣷⣾⣷⣶⣷⣾⣴⣶⣼⡿⣷⣾⣿⣶⣶⣷⣶⣶⣾⣾⣷⣷⣶⣷⣾⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿
⣧⣤⣤⣴⣴⣶⣤⣤⣿⣬⣥⣴⣦⣦⣥⣤⣤⣤⣇⣤⣤⣼⣧⣢⣧⣤⣤⣧⣤⣬⣷⣧⣤⣼⣷⣤⣼⣤⣤⣧⣬⣤⣠⣤⣤⣧⣤⣧⣾⣤⣇⣤⣤⣤⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣆⣍⣹⣉⣉⣉⣍⣿⣉⣉⣞⣟⣹⣏⢉⣉⣙⣯⣻⣋⣏⣍⢉⣹⣈⣨⣋⣙⣉⣉⣀⣏⣿⣀⣉⣉⣏⣁⣀⣹⣘⣹⣉⣉⣁⣈⣙⣏⣁⣁⣉⣽⣇⡏⣉⣉⣉⣈⣉⣉⣉⣻⣈⣉⣇⣐⣀⣘⣀⣇⣁⣀⣉⣍⣏⣿⣿
⡯⠉⠽⠏⠹⡟⢛⠛⣿⠻⣿⠛⢹⠛⢻⠛⠉⠛⠛⡏⠋⢻⡟⠻⠛⠙⠛⠛⠛⠛⠛⡟⡛⠋⠛⠋⢛⠛⡟⠍⠛⠛⠋⢛⡿⠹⠛⠛⠛⠙⠛⠛⠛⣿⠍⠛⠙⠙⠛⠛⣻⡏⠙⠛⢛⠛⢿⠛⠛⠋⣏⠛⠋⠉⠙⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3374

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_14/01/2023:_Dortmund_Moving_to_Free_Software⠀✐


Posted in News_Roundup at 10:25 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Applications
          o Instructionals/Technical
          o WINE_or_Emulation
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o BSD
          o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
          o Rocky_Linux,_Fedora,_and_Red_Hat
          o Debian_Family
          o Devices/Embedded
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Government
          o Web_Browsers/Web_Servers
                # Chromium
          o Programming/Development
                # Perl_/_Raku
                # Python
                # Java
    * Leftovers
    * Security
          o Twitter
          o Privacy/Surveillance
    * Defence/Aggression
    * Transparency/Investigative_Reporting
    * Environment
          o Energy/Transportation
    * Finance
    * AstroTurf/Lobbying/Politics
    * Censorship/Free_Speech
    * Freedom_of_Information_/_Freedom_of_the_Press
    * Civil_Rights/Policing
    * Internet_Policy/Net_Neutrality
    * Digital_Restrictions_(DRM)
    * Monopolies
          o Trademarks
          o Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ GamingOnLinux ☛ System76_teasing_new_fully_AMD_powered
                  Pangolin_Linux_laptop⠀⇛


                       System76 saw your many comments and they’re going
                       to deliver. The Pangolin is making a return,
                       powered by all AMD.


          o § Server⠀➾


                # ⚓ TechTarget ☛ Startup’s_eBPF_APM_tools_turn_up_heat_on
                  Datadog_|_TechTarget⠀⇛


                       Lemonade plans to put tools from eBPF startup
                       Groundcover in production this year in a bid to
                       reduce instrumentation work and other overhead for
                       its small DevOps team.


          o § Applications⠀➾


                # ⚓ Make Use Of ☛ exa:_The_Linux_ls_Replacement_That’s_a_Little
                  Bit_Extra⠀⇛


                       The ls command does its job well. But is there a
                       better and more powerful utility for listing files
                       and folders on Linux?


                       The Linux ls command is something most users use
                       all the time, but they never seem to think it could
                       be improved upon.


                       exa aims to replace this venerable command with a
                       colorful appearance and new features. Will it
                       replace ls for you? Let’s find out!


                # ⚓ GStreamer:_GStreamer_1.21.90_pre-release_(1.22_rc1)⠀⇛


                       The GStreamer team is excited to announce the first
                       release candidate for the upcoming stable 1.22
                       release series.


                       This 1.21.90 pre-release is for testing and
                       development purposes in the lead-up to the stable
                       1.22 series which is now feature frozen and
                       scheduled for release very soon. Any newly-added
                       API can still change until that point, although it
                       is extremely unlikely for that to happen at this
                       point.


                       Depending on how things go there might be more
                       release candidates in the next couple of days, but
                       in any case we’re aiming to get 1.22.0 out as soon
                       as possible.


                       Preliminary release notes highlighting all the new
                       features, bugfixes, performance optimizations and
                       other important changes will be made available in
                       the next few days.


          o § Instructionals/Technical⠀➾


                # ⚓ Joystick_not_detected_after_installing_Amiga_Emulator_fsuae
                  snap_package⠀⇛


                       After installing the Amiga Emulator fsuae via snap,
                       I noticed that the Joystick was not detected.
                       Because snap packages are containerised and
                       isolated from the rest of the system, you need to
                       allow access for the Joystick by viewing the
                       connections list and updating the slot.


                # ⚓ Bypass_with_hexencoding,_dump_/etc/passwd⠀⇛


                # ⚓ Video ☛ How_to_install_Vanilla_OS_|_DIRECTLY_on_Computer,
                  VirtualBox_and_GNOME_Boxes!_(NEW_DISTRO)_–_Invidious⠀⇛


                # ⚓ Linux Capable ☛ How_to_Install_Wine_on_Linux_Mint_21/20⠀⇛


                       Wine is a compatibility layer for running Windows
                       applications on Linux and other Unix-like operating
                       systems. It allows users to run many Windows-based
                       programs on Linux without needing to install a
                       Windows operating system. Wine translates Windows
                       system calls into POSIX-compliant system calls,
                       allowing Windows applications to run on Linux and
                       other Unix-like operating systems.


                       In the following tutorial, you will learn how to
                       install and configure Wine on Linux Mint 21 or
                       Linux Mint 20 release series using the command line
                       terminal by importing the official WineHQ
                       repository and installing the latest stable, which
                       is still at this current time, 7.0 or the staging
                       or development releases which are currently
                       featuring 8.0 onwards.


                # ⚓ LinuxConfig ☛ Troubleshooting_the_Application_not_found
                  error_in_Flatpak⠀⇛


                       The Application not found error may occur in
                       Flatpak on your Linux system for a variety of
                       reasons. This typically happens when the
                       application you are trying to open is not actually
                       installed, or if the installation has been damaged
                       through moving system files or some other means. In
                       this tutorial, we will look at several ways to
                       troubleshoot the Application not found error in
                       Flatpak.


                # ⚓ LinuxConfig ☛ How_to_add_repository_using_Flatpak⠀⇛


                       To get started installing software with Flatpak,
                       you will first need to add one or more software
                       repositories. Flatpak uses these repositories
                       (“remotes” in Flatpak terms) to search for and
                       install software from centralized locations. This
                       behavior should seem familiar to Linux users, as it
                       is exactly how traditional package managers work as
                       well.


                       Developers can create their own Flatpak repos to
                       allow access to their software across all major
                       Linux distros, since Flatpak is distribution
                       independent. You may find yourself in need of
                       adding a Flatpak repo in order to gain access to
                       software not available in your default system
                       repositories, or to subscribe to application
                       download and updates from a particular developer
                       that has chosen to release their software through
                       Flatpak.


                       In this tutorial, we will take you through the step
                       by step instructions to add a repository to Flatpak
                       on a Linux system. Then, we will show how to search
                       the newly configured repository for software that
                       can be installed.


                # ⚓ LinuxConfig ☛ How_to_remove_repository_using_Flatpak⠀⇛


                       Flatpak uses remote repositories (usually just
                       called “remotes”) in order to search for and
                       download software. If at any point you decide that
                       you no longer wish to download applications that
                       come from a particular repository, you can always
                       remove it from Flatpak. This will prevent Flatpak
                       from querying the specified repo for future
                       software searches and updates.


                       It is recommended to only keep Flatpak remotes that
                       you plan to use. Otherwise, your Flatpak
                       configuration can get convoluted with metadata and
                       other irrelevant settings and files that you will
                       not need. The only caveat to keep in mind is that
                       applications which were installed from a removed
                       remote will no longer receive updates, unless it is
                       possible to receive those updates from a different
                       repository that you have added to Flatpak. Previous
                       apps that have been installed from the removed repo
                       will not be uninstalled from your system.


                # ⚓ LinuxConfig ☛ How_to_install_Flatpak_on_CentOS⠀⇛


                       Flatpak is a package manager that is available for
                       installation on CentOS Linux and all other major
                       Linux distros. Flatpak offers CentOS users an
                       alternative to the official repos and default dnf
                       package manager as a source of software
                       installation. Many applications available in
                       Flatpak currently do not reside in official CentOS
                       repos, making this a big benefit of installing
                       Flatpak.


                       To use Flatpak on CentOS, we simply need to install
                       the program, add the repos that contain the flatpak
                       packages you wish to install, and then search for
                       and install the packages. Flatpak will also let us
                       manage and update the apps that we install. Flatpak
                       works the same across all Linux distros, so you
                       will only need to learn the command syntax once.
                       The applications in Flatpak are also distribution
                       independent.


                       In this tutorial, you will see how to install
                       Flatpak package manager on CentOS Linux. Then, we
                       will take you through some basic usage of Flatpak
                       so you can get started with adding repositories and
                       installing custom software of your choice.


                # ⚓ Trend Oceans ☛ What_You_Need_to_Know_About_the_rm_Command
                  in_Linux_and_Its_Advanced_Syntax_–_TREND_OCEANS⠀⇛


                       The rm (remove) command is one of the most
                       important Linux utilities that every beginner to
                       advanced Linux user should understand how it works
                       and how to use it.


                # ⚓ ID Root ☛ How_To_Install_FreeTube_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       FreeTube on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, FreeTube is an open-source software
                       application that provides a more privacy-friendly
                       alternative to YouTube. FreeTube is an open-source
                       software application that provides a more privacy-
                       friendly alternative to YouTube. It prevents Google
                       from tracking your browsing activity with its
                       cookies or JavaScript code so that you can enjoy a
                       stress-free online experience.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the FreeTube on Ubuntu 22.04 (Jammy
                       Jellyfish). You can follow the same instructions
                       for Ubuntu 22.04 and any other Debian-based
                       distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Barry Kauler ☛ First_bootup_2-letter_language_asked_in
                  initrd⠀⇛


                       The method used to translate the scripts in the
                       initrd has varied over the years. At one stage, I
                       tried the gettext method. Prior to now, it has been
                       the “sss” method; “simple string substitution”, in
                       which the strings in a script are completely
                       replaced, resulting in a non-English script.


                       The latter method is clumsy, for various reasons.
                       For example, if you want to change the scripts to a
                       different language, copies of the original scripts
                       in English have to be kept — though, I have
                       implemented a devious method of translating the
                       non-English script back to English, then to another
                       language. There are other problems also.


                # ⚓ Linux Capable ☛ How_to_Install_RPM_Fusion_on_Rocky_Linux
                  EL9/EL8⠀⇛


                       RPM Fusion is a helpful resource for Linux users,
                       providing a comprehensive repository of packages
                       not found in official repositories. Packages span
                       everything from multimedia codecs to proprietary
                       drivers and non-open-source software.


                       The following tutorial will teach you how to
                       install RPM Fusion on Rocky Linux 9 or Rocky Linux
                       8 workstation desktop or headless server so you can
                       install additional open-source or proprietary
                       packages utilizing the command line terminal.


                # ⚓ Trend Oceans ☛ How_to_Fix_Docker:_Unable_to_Prepare
                  Context:_Unable_to_Evaluate_Symlinks_in_the_Dockerfile_Path_–
                  TREND_OCEANS⠀⇛


                       Let’s jump right into the resolution section, where
                       you’ll learn how to fix the “unable to prepare
                       context: unable to evaluate symlinks in Dockerfile
                       path errors” on your Windows or Linux machine.


                # ⚓ FOSSLinux ☛ How_to_install_Docker_on_Fedora_|_FOSS_Linux⠀⇛


                       Docker is one essential and robust version of
                       technologies that is very important for developers
                       and sysadmins these days. This tool allows you to
                       create, deploy and manage lightweight, stand-alone
                       packages known as containers. The containers have
                       the required code, runtime, libraries, system
                       settings, and dependencies to run an app.


                       Docker allows you to categorize apps from your
                       infrastructure to deliver software faster. Using
                       this app, you may manage your infrastructure the
                       same way you do your apps. Take advantage of
                       Docker’s shipping, testing, and deploying code
                       methodologies. You can, by large, do away with or
                       minimize the time between code writing and running
                       it in production.


                # ⚓ FOSSLinux ☛ How_to_properly_uninstall_MySQL_Server_in
                  Ubuntu_|_FOSS_Linux⠀⇛


                       Ubuntu’s package management system makes it very
                       simple to install, upgrade, or remove the software
                       from the system. However, some software packages
                       have many configuration directories and need extra
                       effort to uninstall.


                       The MySQL Server is one such piece of software
                       frequently used in Ubuntu. We cannot use the
                       standard apt purge command to remove the MySQL
                       server from the system entirely. Certain actions
                       must be taken to ensure that MySQL and its
                       components are appropriately removed from the
                       Ubuntu system.


                       We may frequently encounter problems while
                       attempting to start the MYSQL server on a Linux
                       system. There might be several explanations for
                       this. First, sometimes an old configuration file
                       exists in the system and is not correctly erased
                       after uninstalling. Therefore, we must manually
                       remove the MYSQL server and configuration file in
                       that scenario.


                # ⚓ FOSSLinux ☛ How_to_install_and_use_Vim_on_Ubuntu_|_FOSS
                  Linux⠀⇛


                       Vim is a powerful text editor that is preinstalled
                       on most Linux distributions. Ubuntu includes Vim,
                       vi, nano, Gedit (GUI), and numerous other text
                       editors. Vim is an improvised version of the vi
                       text editor. Ubuntu comes with Vim preinstalled.
                       However, the preinstalled version is very basic.


                       To get the full version, we shall use the apt-get
                       or apt command to install it on our Ubuntu
                       operating system. Vim is capable of editing all
                       types of plain text. It is beneficial for editing
                       configuration files and programs written in shell,
                       Python, Perl, C/C++, and other languages. This
                       tutorial will demonstrate how to install and use
                       the vim text editor on Ubuntu Linux.


                       We are utilizing Ubuntu 22.04, the most recent
                       version of Ubuntu. Installation requires executing
                       fundamental Linux commands on the Ubuntu command
                       line (terminal). We used various methods for
                       installing Vim. You may utilize any of these
                       options that you deem fit.


                # ⚓ FOSSLinux ☛ How_to_completely_uninstall_Linux_Mint_from
                  your_PC_|_FOSS_Linux⠀⇛


                       Linux Mint is a community-driven Ubuntu-based Linux
                       distribution packed with various free and open-
                       source software. It can give complete multimedia
                       capability out-of-the-box for those who opt to
                       incorporate proprietary software such as multimedia
                       codecs. So you decided to try out Linux by
                       installing Linux Mint alongside Windows?


                       And for some reason, you’ve decided to undo
                       everything, including uninstalling Linux Mint,
                       cleaning up grub (bootloader), and reverting your
                       PC to its previous Windows-only state? Since I’m a
                       Linux enthusiast, I’m assuming you’re starting over
                       because something went wrong when you were
                       experimenting with Linux, and you want to start
                       from scratch.


          o § WINE or Emulation⠀➾


                # ⚓ Wine_Reviews_:_Wine_development_release_8.0-rc4_is_now
                  available_for_Linux_FreeBSD_and_macOS⠀⇛


                       The Wine development release 8.0-rc4 is now
                       available.


                       What’s new in this release:


                       - Bug fixes only, we are in code freeze.


                       The source is available now. Binary packages are in
                       the process of being built, and will appear soon at
                       their respective download locations.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Google_to_release_a_tool_to_enable
                  Bluetooth_on_the_Stadia_Controller⠀⇛


                       Google is getting ready to shut down Stadia now,
                       their cloud gaming service, but they have some good
                       news for those with the Stadia Controller.


                # ⚓ GamingOnLinux ☛ Deep_Rock_Galactic_sold_2.3_million_copies
                  last_year_and_I’m_not_surprised_–_it’s_awesome⠀⇛


                       Deep Rock Galactic is a game about a bunch of
                       Dwarves going mining, and there’s lots of creepy-
                       crawlies that want to get in the way. It seems to
                       only be getting more popular as time goes on too.


                # ⚓ GamingOnLinux ☛ The_next_release_of_0_A.D._will_have
                  experimental_Vulkan_API_support⠀⇛


                       0 A.D. is an in-development free and open source
                       RTS, one that’s very promising and looks pretty
                       good and the next Alpha version will also feature
                       experimental Vulkan support.


                # ⚓ GamingOnLinux ☛ New_Steam_Linux_&_Steam_Deck_Beta_fixes_up
                  a_major_bug⠀⇛


                       Recently Valve put up a Beta for Steam desktop and
                       Steam Deck, which unfortunately came with a huge
                       bug that people found but a new release fixes it
                       and adds some more fixes too.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ Nate Graham ☛ This_week_in_KDE:_Well_just_look_at_all
                        these_pictures⠀⇛


                             This one is pretty juicy in the eye candy
                             department as we ramp up in the new year!
                             Check out all this goodness…


                             You can now show the Hebrew Calendar in your
                             Digital Clock popup’s calendar if you want…


    * § Distributions and Operating Systems⠀➾


          o § BSD⠀➾


                # ⚓ Klara ☛ 5_Factors_When_Considering_FreeBSD_vs._Linux:
                  Packages⠀⇛


                       A package manager helps with finding, downloading,
                       installing, configuring, updating, and removing
                       third-party applications in a Unix system. This is
                       not too different when looking at Linux vs. FreeBSD
                       packages.


                       A typical invocation starts with the package
                       manager’s name (for example, apt or pkg), followed
                       by a subcommand detailing the action to perform.
                       Package managers typically maintain a local cache
                       of available packages and their current versions,
                       which they periodically synchronize with the
                       package repository.


                       This allows the user to find and install new
                       software, perform simple version upgrades of
                       existing packages, and maintain compatibility with
                       operating system libraries and other dependencies
                       for a specific version of the OS.


                # ⚓ DragonFly BSD Digest ☛ /etc/rc.local.d_now_an_option_–
                  DragonFly_BSD_Digest⠀⇛


                       DragonFly now checks both /etc/rc.d and /etc/
                       rc.local.d during boot and shutdown, so you don’t
                       have to mix system-installed and local rc scripts.


                # ⚓ Frederic Cambus ☛ NetBSD_ASCII_flag_for_the_bootloader_|
                  Frederic_Cambus⠀⇛


                       As mentioned in my “Customizing NetBSD boot
                       banners” article, it’s really easy to customize
                       NetBSD boot banners using the boot.cfg
                       configuration file.


                       In a previous life, I used to draw ASCII art
                       (mostly in the pre-2000 era) and more precisely a
                       type of ASCII art referred as newschool ASCII in
                       the artscene. By taking advantage of the extended
                       character set (the 128 to 255 range) of the IBM
                       PC’s code page 437, it was possible to achieve
                       great detail and really smooth curves. Some
                       examples can be found at the bottom of my online
                       gallery.


          o § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾


                # ⚓ Introducing_OpenMandriva_Lx_ROME:_The_Rolling-Release
                  Edition_of_OpenMandriva_Linux_–_LinuxWizardry⠀⇛


                       The OpenMandriva team has announced the general
                       availability of OpenMandriva Lx ROME, their
                       rolling-release edition of this independently
                       developed GNU/Linux distribution descendant from
                       Mandriva Linux. This distribution is aimed at
                       bleeding-edge users who want to have the latest and
                       greatest GNU/Linux technologies without upgrading
                       or reinstalling.


                       OpenMandriva Lx ROME is a unique and independent
                       distribution, not based on any other Linux
                       distribution. A direct descendant of Mandriva
                       Linux, it was the first Linux distribution to
                       utilize the LLVM compiler. This release continues
                       to use the entire LLVM toolchain, which completes
                       the work that began in 2015, even before Android
                       switched its compilers.


                       Powered by the latest and greatest Linux 6.1 kernel
                       series (Clang-compiled, of course), OpenMandriva’s
                       rolling-release edition is available in two spins
                       featuring the popular KDE Plasma and GNOME desktop
                       environments. The Plasma spin comes with the KDE
                       Plasma 5.26.4 desktop environment, which is
                       accompanied by the KDE Frameworks 5.101 and KDE
                       Gear 22.12 software suites, modified to handle the
                       new JPEG-XL file format. On the other hand, the
                       GNOME spin features the latest GNOME 43.2 desktop
                       environment on top of Wayland.


          o § Rocky Linux, Fedora, and Red Hat⠀➾


                # ⚓ How_to_Run_Metabase_and_Nginx_as_a_Reverse_Proxy_on_Rocky
                  Linux_9_–_LinuxWizardry⠀⇛


                       Metabase is a user-friendly and open-source
                       business intelligence tool that allows you to
                       analyze data. It is widely used for sharing
                       automated reports, live dashboards, and business
                       questions with many organizations.


                       This tutorial will explain how to set up Metabase
                       using a jar file and configure Nginx for a reverse
                       proxy on Rocky Linux 9.


                # ⚓ ID Root ☛ How_To_Install_Nmap_on_Rocky_Linux_9_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Nmap on Rocky Linux 9. For those of you who didn’t
                       know, Nmap is a powerful tool that is widely used
                       by network administrators and security
                       professionals to scan networks and perform security
                       assessments. It is available for various platforms,
                       including Linux, Windows, and macOS.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of Nmap Network Scanner on Rocky
                       Linux. 9.


                # ⚓ LinuxConfig ☛ An_Introduction_to_Flatpak_App_Bundles⠀⇛


                       Ordinarily, Flatpak is utilized by querying online
                       repositories for software to download and install.
                       Installing an application from a repository (like
                       FlatHub) means that it is very easy to maintain
                       updates for the application and others that have
                       been installed via Flatpak. However, Flatpak also
                       gives us the option to install individual
                       applications with the .flatpak extension.


                       This can be useful in situations where a developer
                       has created some software that can be installed
                       with Flatpak, but has not yet uploaded the
                       application to a central repository for
                       distribution and organized updates. These
                       individual installations are distributed in what is
                       called single-file bundles.


                       In this tutorial, you will learn how to get started
                       with Flatpak app bundles by seeing how to create an
                       app bundle and install it with Flatpak on a Linux
                       system.


                # ⚓ LinuxConfig ☛ Flatpak_vs_FlatHub:_A_Comparison_of_Linux_App
                  Installers⠀⇛


                       Flatpak is a universal package management tool for
                       Linux systems, which is meant to streamline the
                       process of searching for and installing
                       applications regardless of what Linux distro you
                       are using. Despite making things easier, there is a
                       small learning curve to getting started with
                       Flatpak, partly because of the lingo that gets
                       tossed around with “remotes” and external repos
                       like FlatHub. For users that are brand new to
                       Flatpak, you may be wondering how FlatHub fits into
                       the equation.


                       In this tutorial, you will learn about the
                       difference between Flatpak and FlatHub, and how
                       both technologies work together to provide you with
                       a big catalog of software applications that can be
                       installed regardless of what Linux distribution you
                       are running. We will also look at how Flatpak
                       differs from some other popular distribution
                       independent package installers, like Snap.


                # ⚓ Enable_Libvirt_rw_socket_on_RHEL9⠀⇛


                # ⚓ Security Week ☛ Red_Hat_Announces_General_Availability_of
                  Malware_Detection_Service_|_SecurityWeek.Com⠀⇛


                       Red Hat announced on Tuesday the general
                       availability of a malware detection service for Red
                       Hat Enterprise Linux (RHEL) systems.


                       The Insights service, created in partnership with
                       IBM X-Force, scans RHEL systems for malware using a
                       database of more than 180 signatures associated
                       with known Linux malware. Users can obtain
                       aggregated results for all their systems or results
                       for individual system scans.


                       RHEL 8 and 9 hosts are supported. Scans can be run
                       manually, but they can also be scheduled or
                       automated.


          o § Debian Family⠀➾


                # ⚓ The Anarcat ☛ Evaluating_suspend_battery_use_with_systemd_–
                  anarcat⠀⇛


                       This is a quick hack that will allow you to do some
                       (manual) computations on power usage during suspend
                       on your laptop, using systemd hooks.


                       It might be possible to use a similar hack on non-
                       systemd systems of course, you just need something
                       that fires a hook on suspend and resume.


                # ⚓ bibata_cursor_theme_is_available_on_Debian_(unstable)_–
                  ひとりしずかに。⠀⇛


                       Recently bibata cursor theme is available on Debian
                       (unstable)


                # ⚓ The Anarcat ☛ Antoine_Beaupré:_20_years_blogging⠀⇛


                       Many folks have woken up to the dangers of
                       commercialization and centralisation of this very
                       fine internet we have around here. For many of us,
                       of course, it’s one big “I told you so”…


                       [...]


                       The best years in terms of numbers are the first
                       two years (2005 and 2006, I didn’t check the
                       numbers on earlier years), but I doubt they are the
                       best in terms of content. Really, the best writing
                       I have ever did was for LWN. I dare hope I have
                       kept the quality I was encouraged (forced?) to
                       produce, but I know I cannot come anywhere close to
                       what the LWN editors were juicing out of me. You
                       can also see that I immediately dropped to a more
                       normal 27 article in 2019, once I stopped writing
                       for LWN…


                       [...]


                       Interestingly, I wrote a lot in 2022. People
                       sometimes ask me how I manage to write so much: I
                       don’t actually know. I don’t have a lot of free
                       time on my hand, and even less than before in the
                       past two years, but somehow I keep feeding this
                       blog.


                # ⚓ Rebooting…_–_Matt_Brown⠀⇛


                       After nearly 7 years of dormancy, I’m rebooting
                       this website and have a goal to write regularly on
                       a variety of topics going forward. More on that and
                       my goals in a coming post…


                       For now, this is just a placeholder note to help
                       double-check that everything on the new site is
                       working as expected and the letters are flowing
                       through the “pipes” in the right places.


                # ⚓ Diziet ☛ diziet_|_SGO_(and_my)_VPN_and_network_access_tools
                  –_in_bookworm⠀⇛


                       Recently, we managed to get secnet and hippotat
                       into Debian. They are on track to go into Debian
                       bookworm. This completes in Debian the set of VPN/
                       networking tools I (and other Greenend) folks have
                       been using for many years.


          o § Devices/Embedded⠀➾


                # ⚓ Engadget ☛ Raspberry_Pi’s_new_12-megapixel_camera_modules
                  provide_powered_autofocus_|_Engadget⠀⇛


                       Raspberry Pi has launched the Camera Module 3 with
                       big improvements, including higher resolution,
                       infrared, HDR, autofocus and more..


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Camera_Module_v3_Review:_A
                  New_Angle_on_Photography⠀⇛


                       The latest camera from Raspberry Pi brings
                       autofocus, HDR and a new wide angle lens that
                       captures every angle.


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_Produced_10_Million_RP2040s
                  in_2021,_More_Pi_Stores_Likely⠀⇛


                       In a recent episode of Tom’s Hardware: The Pi Cast,
                       Raspberry Pi CEO Eben Upton revealed that 10
                       million RP2040 chips have been made since 2021 and
                       that there could be more Raspberry Pi stores
                       opening in the future.


                # ⚓ Raspberry Pi ☛ Mice_explore_virtual_worlds_with_a_Raspberry
                  Pi-powered_VR_headset⠀⇛


                       A Raspberry Pi 4 runs the Godot video game engine
                       inside the headset, and the mice view the output
                       through a dual-SPI display. Researchers created
                       virtual scenes in Godot to test the ability of mice
                       in various scenarios, such as avoiding VR cliffs
                       and reacting to looming objects of various sizes
                       coming towards them at different speeds.


                # ⚓ Linux Gizmos ☛ ESP32_compact_board_integrates_Walkie-Talkie
                  module⠀⇛


                       LILYGO recently launched a tiny ESP32-S3 device
                       equipped with a Walkie-Talkie module and other
                       peripherals such as an OLED display, a speaker and
                       a mic and a 18650 battery holder. The company also
                       featured an ESP32 device with a touch-screen LCD
                       display equipped with a stylus pen.


                # ⚓ Hackaday ☛ Arduino_Library_Brings_Rtl_433_To_The_ESP32⠀⇛


                       If you have an RTL-SDR compatible radio there’s an
                       excellent chance you’ve heard of the rtl_433
                       project, which lets you receive and decode signals
                       from an ever-expanding list of supported devices in
                       the ISM radio bands. It’s an incredibly useful
                       piece of software, but the fact that it requires an
                       external software defined radio and a full-fledged
                       computer to run dictated the sort of projects it
                       could realistically be used for.


                # ⚓ CNX Software ☛ 433_MHz_is_not_dead!_Using_an_ESP32_board
                  with_LoRa_module_to_talk_to_433_MHz_sensors_–_CNX_Software⠀⇛


                       Everyone is talking about Matter, Bluetooth,
                       Zigbee, and Zwave, but before these complex
                       communication technologies, we had one simple,
                       robust one that our sensors and devices used to
                       leverage: 433MHz. It may be too simplistic to talk
                       about 433 MHz as a technology as there are
                       different and various usages of this frequency. You
                       can find it being used in numerous devices around
                       your home, from your outdoor temperature sensors,
                       and security sensors to the tire pressure sensors
                       in your car.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Notebook Check ☛ FiiO_M11S:_Digital_audio_player_launches
                  with_Android_10_and_Snapdragon_660_SoC_–_NotebookCheck.net
                  News⠀⇛


                # ⚓ Ars Technica ☛ New_Sony_Walkman_music_players_feature
                  stunning_good_looks,_Android_12_|_Ars_Technica⠀⇛


                # ⚓ GSM Arena ☛ Nothing_Phone_(1)_gets_second_Android_13_beta_–
                  GSMArena.com_news⠀⇛


                # ⚓ Phone Arena ☛ Android_13_QPR2_Beta_may_add_the_ability_to
                  change_Pixel_lockscreen_shortcuts_–_PhoneArena⠀⇛


                # ⚓ Nokia Mob ☛ New_Android_Build_makes_Nokia_T20_more_stable_|
                  Nokiamob⠀⇛


                # ⚓ Android Authority ☛ Motorola_Moto_G_Play_(2023)_review:
                  Limited_reach_–_Android_Authority⠀⇛


                # ⚓ 9to5Google ☛ ChromeOS_109_rolling_out_with_a_tweak_to_how
                  Android_apps_launch⠀⇛


                # ⚓ India Times ☛ Google_reiterates:_CCI_is_‘bad’_for_Android
                  smartphone_users_in_India_–_Times_of_India⠀⇛


                # ⚓ India Today ☛ Google_says_Android_smartphones_will_get
                  expensive,_warns_of_threat_to_user_security:_here’s_why_–
                  India_Today⠀⇛


                # ⚓ Ubuntu Pit ☛ 7_Best_Journal_Apps_for_Android_|_Track_Your
                  Daily_Life⠀⇛


                       Journaling has always been a popular activity for
                       people looking to express their thoughts, feelings,
                       and experiences in a more structured and meaningful
                       way. With the proliferation of Android devices,
                       like smartphones and tablets, it is now easier to
                       keep a journal on the go. Thanks to the numerous
                       journal apps available for Android users. This kind
                       of app makes journaling convenient and efficient.
                       This article will explore some of the best journal
                       apps for Android, which will help you live more
                       organized and meaningfully.


    * § Free, Libre, and Open Source Software⠀➾


          o ⚓ Trail Of Bits ☛ Keeping_the_wolves_out_of_wolfSSL⠀⇛


                 The vulnerabilities mark a milestone for the fuzzer: They
                 are the first vulnerabilities found using this tool that
                 have a far-reaching impact. We can also confidently say
                 that this vulnerability would not have been easy to find
                 with classical bit-level fuzzers. It’s especially
                 intriguing that on average, the fuzzer took less than one
                 hour to discover a vulnerability and crash.


          o ⚓ Anders Borch ☛ Is_Mastodon_Development_Sustainable?⠀⇛


                 At the time of this writing Mastodon has over 3.400 open
                 issues, and over 200 open pull requests.


                 We need a better way to keep Mastodon development moving
                 forward.


                 Who gets to decide which of the 200 open PRs are worthy
                 of being included in the main distribution? How do we
                 find the resources to go through all those open issues?


          o ⚓ Derek_Powazek_–_A_community_isn’t_a_garden,_it’s_a_bar.⠀⇛


                 I’ve been writing about social media since it was called
                 virtual community, and in that time, the most common
                 metaphor I’ve used is gardening. It’s a good metaphor,
                 because it demands a delineation between what you want to
                 grow and what you don’t, and it emphasizes nurturance,
                 perhaps the most important quality of a community
                 manager.


                 But it’s almost 2023 now. The world is different, the
                 online world is very different, and I’m pushing 50. So I
                 think it’s time we all start talking about online
                 gathering places with a more apt metaphor: bars.


                 [...]


                 The parallels to online behavior are easy to see. Online,
                 people are much more willing to type things that they’d
                 never say in person. How many times have we found out the
                 hard way that a celebrity really cannot handle having a
                 Twitter account? Drunk on the feedback loop, they can be
                 goaded into saying more and more extreme things.


                 In a virtual space, when everyone is being noisy, you
                 have to be even louder to get noticed. This is what leads
                 to the loudest, most aggressive people gaining the most
                 attention online.


                 Online or off, you have to speak above the din just to be
                 heard, and that inevitably coarsens the conversation.
                 Which brings us to the people there to protect us from
                 the loud and stupid.


          o § Government⠀➾


                # ⚓ Joinup ☛ A_new_step_towards_Open_Source_for_Dortmund⠀⇛


                       It is through the working group on Free Software
                       that the initial recommendation for a Coordination
                       body for Open Source was suggested in October last
                       year. Mentioned in the “Roadmap Memorandum zur
                       Digitalisierung 2020 – 2025” of the city, this
                       suggestion builds upon a declaration of the German
                       Ministry of Interior on the need for stronger
                       digital sovereignty. This Coordination Unit will
                       first conduct some research work on how to best
                       implement Open Source solutions in the city
                       administration. This unit will be responsible for
                       developing open source governance as a cross-
                       sectional task of the city administration, in
                       cooperation with the Kommunale Gemeinschaftsstelle
                       für Verwaltungsmanagement (KGSt).


          o § Web Browsers/Web Servers⠀➾


                # § Chromium⠀➾


                      # ⚓ Google ☛ Chrome_Releases:_Stable_Channel_Update_for
                        ChromeOS_/_ChromeOS_Flex⠀⇛


                             The Stable channel is being updated to
                             109.0.5414.94 (Platform version: 15236.66.0)
                             for most ChromeOS devices and will be rolled
                             out over the next few days.


          o § Programming/Development⠀➾


                # ⚓ Architecture_diagrams_should_be_code⠀⇛


                       For the past few years I’ve been the most senior
                       developer on my teams in Atlassian, in both
                       position (Principal Engineer) and time (almost 9
                       years) – this means I usually take on the
                       responsibility of managing our software
                       architecture.


                       Architecture is the relationships between systems,
                       which can be fairly tricky to talk about. Probably
                       the best form of communication is a diagram, with
                       boxes representing systems (or components) and
                       lines representing relationships between them. This
                       can still have issues.


                # ⚓ Epochalypse⠀⇛


                       The signed 32-bit integer that is historically used
                       to keep unix epoch time has already exhausted of
                       all possible values.


                # ⚓ Introduction_–_Just_Programmer’s_Manual⠀⇛


                # ⚓ Makefiles_for_Web_Work_–_Ross_Zurowski⠀⇛


                       A set of recipes for using Makefiles for web
                       development.


                # ⚓ What_Happens_When_A_CPU_Starts⠀⇛


                # ⚓ How_to_store_your_app’s_entire_state_in_the_url⠀⇛


                       I’m working on a flowchart editor that runs in the
                       browser, and I wanted a way for people to use it
                       without having to sign in, or store any data on our
                       server. I wanted to give them control over their
                       data and to be able to store it locally to open and
                       edit later. And also easily share it with other
                       people. It’s easy to do this by supporting file
                       upload/download, but I wanted something simpler,
                       like the ability to share by sending a url. I also
                       didn’t want to store anything on the backend (at
                       least for the free tier).


                       [...]


                       Everything after the `/g/a#` is a stringified
                       version of a json object that contains all the
                       information about the flowchart. It gets
                       stringified, then compressed, then Base64 encoded.
                       I update the url on every graph edit, so copying
                       the graph state is as simple as copying the url in
                       your browser bar.


                # ⚓ Jason Swett ☛ What_causes_flaky_tests⠀⇛


                       A flaky test is a test that passes sometimes and
                       fails sometimes, even though no code has changed.


                       In other words, a flaky test is a test that’s non-
                       deterministic.


                       A test can be non-deterministic if either a) the
                       test code is non-deterministic or b) the
                       application code being tested is non-deterministic,
                       or both.


                # ⚓ Daniel Lemire ☛ Care_is_needed_to_use_C++_std::optional
                  with_non-trivial_objects⠀⇛


                       It is possible for an optimizing compiler to elide
                       some or all of the superfluous constructions,
                       especially if you can inline the functions, so that
                       the compiler can see the useless work and prune it.
                       However, in general, you may encounter inefficient
                       code.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ The_Perl_Toolchain_Summit_is_back_in_2023!_|
                        BooK_[blogs.perl.org]⠀⇛


                             After a three years pandemic-induced hiatus,
                             it is my pleasure to announce that the Perl
                             Toolchain Summit is happening again!


                             This year, for the thirteenth edition, we
                             will be gathering again in Lyon, from
                             Wednesday April 27 to Sunday April 30 2023,
                             in the hotel Campanile Lyon Centre Part-Dieu.
                             Participants will stay at the hotel, and work
                             in the meeting rooms dedicated for the event.


                             [...]


                             The summit provides dedicated time to work on
                             the critical systems and tools, with all the
                             right people in the same room. The attendees
                             hammer out solutions to thorny problems and
                             discuss new ideas to keep the toolchain
                             moving forward.


                             Given the important nature of the attendees’
                             work and their volunteer status, we try to
                             pay for all expenses (travel, lodging, food,
                             etc.) through sponsorship. If you’re
                             interested in helping sponsor the summit,
                             please get in touch with Philippe Bruhat at
                             book at cpan.org.


                # § Python⠀➾


                      # ⚓ I_scanned_every_package_on_PyPi_and_found_57_live_AWS
                        keys_|_Tom_Forbes⠀⇛


                             After inadvertently finding that InfoSys
                             leaked an AWS key on PyPi I wanted to know
                             how many other live AWS keys may be present
                             on Python package index.


                # § Java⠀➾


                      # ⚓ OpenSource.com ☛ A_4-minute_guide_to_Java_loops⠀⇛


                             A while loop performs a set of tasks for as
                             long as some predefined condition is true.
                             This is considered a control structure that
                             directs the flow of a program. It’s a way for
                             you to tell your code what to do by defining
                             a condition that it can test, and take action
                             based on what it finds. The two kinds of
                             while loops in Java are while and do while.


    * § Leftovers⠀➾


          o ⚓ Common Dreams ☛ Senate_Democrats_Demand_Answers_From_Southwest
            About_Holiday_‘Meltdown’⠀⇛


                 A group of 15 U.S. senators on Thursday demanded answers
                 from Southwest Airlines’ CEO regarding the company’s
                 management of the disastrous 2022 holiday season, when
                 thousands of travelers were stranded in airports amid
                 nearly 16,000 flight cancelations.


          o ⚓ Common Dreams ☛ Still_Waiting_for_Freedom:_A_Review_of_P.
            Sainath’s_The_Last_Heroes⠀⇛


                 Here’s one possible trajectory for ambitious print
                 journalists. After making your name with aggressive
                 reporting at a smaller newspaper, move up the ladder
                 until you are at a top paper with a prestige beat. Go on
                 the television talk shows to pontificate. Maybe snag a
                 regular column. Offer analyses that seem critical but
                 make sure never to challenge the conventional wisdom.
                 Hire an agent who can get you handsome speaking fees on
                 the lecture circuit.


          o ⚓ The Nation ☛ Norman_Fruchter_Was_a_Giant_in_the_Fight_for
            Education_Equity⠀⇛


                 Norman Fruchter, who died on January 4 from complications
                 after being struck by a car while walking his dog, was a
                 civil rights activist, community organizer, novelist,
                 filmmaker, and for over five decades a giant in the
                 education equity movement. He was 85.


          o ⚓ The Nation ☛ Babylon,_Streaming_Residuals,_and_the_Boss’s
            Hollywood⠀⇛


                 Damien Chazelle’s Babylon is a clash of nostalgias. It’s
                 where the #TCMparty crowd of Singin’ in the Rain meets
                 the #TCMorgy fans of Kenneth Anger’s wallow in grime and
                 degradation, Hollywood Babylon. Chazelle’s Babylon stars
                 Diego Calva as Manny Torres, a young studio fixer and
                 eventual studio boss; Margot Robbie as a self-invented
                 star who becomes an actual star, Nellie LaRoy; and Brad
                 Pitt as Jack Conrad, the reigning king of silent
                 Hollywood. Conrad talks excitedly and vapidly about
                 silent film and wanting to reinvent the form; then the
                 monkey’s paw curls and gives him talkies.


          o ⚓ Hackaday ☛ An_E-Ink_Progress_Bar_For_Your_Unborn_Child⠀⇛


                 Having a child is a major milestone in a person’s life,
                 and there’s a long list of things to get done before that
                 little bundle of joy kicks and screams its way into the
                 world. What better way to make sure you’ve still got time
                 to paint the nursery and assemble the crib than to have
                 an automated loading screen that shows just how far along
                 the organic 3D printing process is?


          o § Science⠀➾


                # ⚓ The Conversation ☛ Eye_movement_science_is_helping_us_learn
                  about_how_we_think⠀⇛


                       For most of human history if you wanted to know
                       what was going on behind someone’s eyes you had to
                       make your best guess. But since the 1960s
                       scientists have been studying the way eye movements
                       may help decode people’s thoughts. The ability to
                       eavesdrop on the details of people’s daydreams and
                       internal monologues is still science fiction. But
                       research is helping us learn more about the
                       connections between our eyes and our mental state.


                       Most recently, research in Germany showed eye
                       tracking could help detect where someone is at in
                       their thinking process.


          o § Education⠀➾


                # ⚓ Zimbabwe ☛ BongoHive,_a_Zambian_Tech_innovation_hub_is
                  hosting_a_webinar_for_Zimbabwean_businesses_small_and
                  large.⠀⇛


                       BongoHive, a Zambia Technology Innovation hub is
                       hosting an information-sharing webinar in
                       partnership with the World Bank and Ministry of
                       Women Affairs, Community, Small and Medium
                       Enterprises. The webinar will be taking place on
                       Friday the 13th of January 2023 at 2pm and is open
                       for anyone to attend.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ A_Medieval_Gothic_Monastery_Built_Using_CAD_/
                  CAM⠀⇛


                       Just because you’re a monk doesn’t mean you can’t
                       use CAD. The Carmelite monks of Wyoming are
                       building a grandiose Gothic Monastery, and it’s awe
                       inspiring how they are managing to build it.


                # ⚓ Hackaday ☛ DIY_Fiber_Laser_Adds_Metal_Cutting_To_The_Mix⠀⇛


                       Sadly, the usual CO2-powered suspects in the DIY
                       laser cutter market are woefully incapable of
                       cutting metal. Sure, they’ll cut the heck out of
                       plywood and acrylic, and most will do a decent job
                       at engraving metal. But cutting through a sheet of
                       steel or aluminum requires a step up to much more
                       powerful fiber laser cutters. True, the costs of
                       such machines can be daunting, but not daunting
                       enough for [Travis Mitchell], who has undertaken a
                       DIY fiber laser cutter build that really caught our
                       eye.


                # ⚓ Hackaday ☛ Swap_The_Clock_Chip_On_The_Mac_SE/30_With_An
                  ATTiny85⠀⇛


                       As [Phil Greenland] explains in the first part of
                       his excellent write-up, the lithium battery used to
                       keep the real-time clock (RTC) going on the
                       Macintosh SE/30 has a nasty habit of exploding and
                       leaking its corrosive innards all over the board.
                       Looking to both repair the damage on a system
                       that’s already had a battery popped and avoid the
                       issue altogether on pristine boards, he started
                       researching how he could replace the battery with
                       something a bit more modern.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Locus Magazine ☛ Commentary:_Cory_Doctorow:_Social
                  Quitting⠀⇛


                       Today, it’s getting harder to believe that these
                       networks will last forever. In the blink of an eye,
                       they’ve gone from unassailable eternal mountains to
                       shifting sands that might blow away at any time.
                       Users are scrambling to download their data and
                       tell their friends where they can be found if
                       (when?) the service disappears.


                       How did these systems go from permanent to
                       ephemeral? How did it happen so quickly?


                       Here’s my theory.


                # ⚓ Common Dreams ☛ ‘We’re_Fighting_Back’:_California_Sues
                  Pharma_Giants_Over_Insulin_Price_Gouging⠀⇛


                       The California Justice Department on Thursday sued
                       three large pharmaceutical companies as well as
                       several major pharmacy benefit managers for
                       unlawfully coordinating to drive up the cost of
                       insulin, a lifesaving medication that patients in
                       the United States are often forced to ration due to
                       high prices.


                # ⚓ TruthOut ☛ California_Sues_Pharma_Giants_Over_Inflated
                  Insulin_Prices⠀⇛


                # ⚓ Meduza ☛ Alexey_Navalny_visited_by_head_of_tuberculosis
                  hospital_—_Meduza⠀⇛


                       On January 13, Ivan Kolotushkin, head of
                       Tuberculosis Hospital no. 1 in Vladimir Colony no.
                       3, visited Alexey Navalny, who has reportedly
                       fallen ill in the punishment cell of Penal Colony
                       no. 6. This, according to Navalny lawyer Vadim
                       Kobzev.


                # ⚓ TruthOut ☛ Wisconsin_Republicans_Refuse_to_Consider
                  Legalizing_Recreational_Cannabis_Use⠀⇛


                # ⚓ TruthOut ☛ NYC_Nurses’_Deal_Is_Just_a_Start_—_Health_Care
                  Advocates_Demand_Major_Reforms⠀⇛


                # ⚓ Hackaday ☛ Detecting_Algal_Blooms_With_The_Help_Of_AI⠀⇛


                       Harmful Algal Blooms (HABs) can have negative
                       consequences for both marine life and human health,
                       so it can be helpful to have early warning of when
                       they’re on the way. Algal blooms deep below the
                       surface can be especially difficult to detect,
                       which is why [kutluhan_aktar] built an AI-assisted
                       algal bloom detector.


                # ⚓ Video ☛ Immunology_101⠀⇛


          o § Proprietary⠀➾


                # ⚓ Shopify_encourages_employees_to_say_no_to_meetings⠀⇛


                       The successful switch to full-time remote work as a
                       result of the pandemic would not have been possible
                       without virtual meeting technology.


                       Technology like Webex, Zoom and Microsoft Teams
                       enabled distributed teams to stay connected and
                       collaborate with each other.


                       But meeting tech is far from a silver bullet – over
                       meeting and back to back video calls have become a
                       major issue. It has caused so-called ‘Zoom fatigue’
                       and distracted employees from focused, productive
                       work.


                # ⚓ The Register UK ☛ Microsoft_to_offer_unlimited_time_off_for
                  US_staff⠀⇛


                       Microsoft is to allow US staff to take unlimited
                       time off in a policy change that is supposed to
                       give them more flexibility but, unsurprisingly,
                       will also have a cost benefit to Redmond.


                       “How, when, and where we do our jobs has
                       dramatically changed,” wrote Kathleen Hogan, chief
                       people officer at Microsoft in a memo to staff,
                       reported first by The Verge. “And as we’ve
                       transformed, modernizing our vacation policy to a
                       more flexible model was a natural next step.”


                       Starting next week, the Windows giant is saying
                       goodbye to its four-weeks-a-year policy for US-
                       based salaried employees. Workers will be given 10
                       days of corporate holidays, alongside unlimited
                       leave. They will also be allowed leave for
                       sickness, mental health issues, bereavement and
                       jury services.


                       New Microsoft employees will not need to wait to
                       accrue holidays.


                       Anyone with unused holiday entitlement will receive
                       a one-time payment for this in April, Microsoft
                       confirmed. Contractors paid by the hour will not be
                       subject to this policy.


                       The move isn’t unique: it brings Microsoft in line
                       with LinkedIn, which it purchased for $26.6 billion
                       in 2016, and a raft of other big businesses
                       including Oracle, Salesforce, Goldman Sachs, and
                       Netflix.


                # ⚓ The Register UK ☛ Microsoft_messes_up_security_upgrade_for
                  Japan,_China,_Korea⠀⇛


          o ⚓ India Times ☛ This_industry_in_India_was_‘most_targeted’_by
            hackers_in_2022 [iophk: Windows TCO]⠀⇛


                 Check Point Research (CPR) says that these cyberattacks
                 were driven by smaller, more agile hackers and ransomware
                 gangs. The cybercriminals focused on exploiting
                 collaboration tools used in work-from-home environments
                 and targeted education institutions that shifted to
                 online learning post-Covid-19.


          o ⚓ India Times ☛ Global_cyberattacks_up_by_38%,_healthcare_most
            targeted_in_India:_Report⠀⇛


                 The report said that hackers like to target hospitals
                 because they perceive them as short on cyber security
                 resources with smaller hospitals particularly vulnerable,
                 as they are underfunded and understaffed to handle a
                 sophisticated cyberattack.


          o ⚓ [Old] Health-ISAC ☛ Chinese_[Crackers]_Exploit_Citrix
            Vulnerabilities⠀⇛


                 U.S. federal authorities and Citrix both are urging users
                 to patch the flaw, tracked as CVE-2022-27518.


                 “These vulnerabilities are known to be actively exploited
                 by a Chinese state-sponsored advanced persistent threat,”
                 says the Department of Health and Human Services’ Health
                 Sector Cybersecurity Coordination Center in an alert
                 issued Friday.


          o ⚓ Hollywood Reporter ☛ Attack_of_the_Chatbots:_Screenwriters’
            Friend_or_Foe?⠀⇛


                 Is ChatGPT a sign that automation is coming to film and
                 TV writing? As far-fetched as it sounds, the arrival in
                 November 2022 of a free prototype of the AI-powered
                 chatbot — which has jolted observers with the
                 sophisticated, fluid writing it can produce when
                 prompted, even in the form of poems, essays and, yes,
                 short scripts — has set off alarm bells about the
                 disruption that the chatbot could wreak on the work of
                 entertainment scribes. Still, top film and TV writers are
                 skeptical that the technology in its current state
                 imperils their livelihoods in any way, even as they
                 remain cautious about the potential for future
                 advancements.


    * § Security⠀➾


          o ⚓ Security Week ☛ Most_Cacti_Installations_Unpatched_Against
            Exploited_Vulnerability_|_SecurityWeek.Com [Ed: It is already
            patched. So the issue here is not Cacti itself. Focus-shifting.]⠀⇛


                 The vast majority of internet-exposed Cacti installations
                 are vulnerable to a critical-severity command injection
                 vulnerability already exploited in attacks.


          o ⚓ Farewell_to_an_Era:_Linux_Kernel_4.9_Ends_Its_6-Year_Support
            Cycle_–_LinuxWizardry⠀⇛


                 The Linux 4.9 kernel series has finally reached its end
                 of life with the release of the 4.9.337 update, which was
                 announced earlier this morning by renowned kernel
                 developer Greg Kroah-Hartman. This marks the end of a
                 six-year journey for Linux kernel 4.9, which was first
                 released on December 11th, 2016.


                 The 4.9 kernel series brought with it a plethora of new
                 features and improvements such as support for shared
                 extents and copy-on-write support on the XFS file system,
                 a hardware latency tracer to detect firmware-induced
                 latencies, support for the Greybus bus from Project Ara,
                 a more efficient BPF profiler, a new optional BBR TCP
                 congestion control algorithm, virtually mapped kernel
                 stacks, and more.


                 Due to its long-term support (LTS) status, Linux kernel
                 4.9 was widely used on mass-production devices by big
                 companies that produce hardware powered by a Linux-based
                 operating system. However, with the release of newer
                 kernels that include all the features of Linux kernel 4.9
                 and more, it is time for users to upgrade their systems.


          o ⚓ Urgent:_Patch_Ubuntu_Linux_Vulnerabilities_with_Latest_Kernel
            Security_Updates_–_LinuxWizardry⠀⇛


                 It is imperative that all Ubuntu Linux users take note of
                 the recent kernel security updates that have been made
                 available for all supported releases of the operating
                 system. These updates are aimed at addressing an even
                 greater number of vulnerabilities and security issues to
                 ensure that your machines are as secure as possible.


                 The new kernel security updates come just a week after
                 the previous batch, which was a significant release that
                 addressed over 20 vulnerabilities. These updates are
                 available for Ubuntu 22.10, Ubuntu 22.04 LTS, Ubuntu
                 20.04 LTS, Ubuntu 18.04 LTS, as well as Ubuntu 16.04 ESM
                 and Ubuntu 14.04 ESM systems.


                 One of the main vulnerabilities addressed in these kernel
                 updates are two Bluetooth flaws, specifically CVE-2022-
                 42896 and CVE-2022-45934. The first vulnerability,
                 discovered by Tamás Koczka, includes multiple use-after-
                 free vulnerabilities in the Bluetooth L2CAP handshake
                 implementation. The second vulnerability, an integer
                 overflow vulnerability, was discovered in the Bluetooth
                 subsystem. These vulnerabilities affect all supported
                 Ubuntu releases and could potentially allow a physically
                 proximate attacker to cause a denial of service (system
                 crash) or even execute arbitrary code.


          o § Twitter⠀➾


                # ⚓ Business Standard ☛ Musk_to_reveal_Twitter_code_as_users
                  unable_to_login_via_third_party_apps⠀⇛


                       Musk said that Twitter will publish tweet
                       recommendation code and make account/tweet status
                       visible no later than next month.


                # ⚓ Techdirt ☛ Latest_Twitter_Problem:_Its_API_Has_Been_Down
                  And_No_Info_Has_Been_Provided⠀⇛


                       Last night, I saw a bunch of folks complaining that
                       the various apps through which they accessed
                       Twitter, were no longer working. People using
                       Tweetbot, Twitteriffic, Tweeten, and others all
                       noted that they were blocked from actually using
                       those services to read Twitter. It quickly became
                       clear that Twitter’s API was completely down. There
                       was plenty of speculation that (in a repeat of an
                       earlier era when Twitter greatly limited its API
                       access out of a fear of losing control of the
                       service to third party developers) that Elon Musk
                       was doing this on purpose to try to stop third
                       party app developers from offering ad-free access
                       to Twitter. However, that still seems like pretty
                       broad speculation.


                # ⚓ Techdirt ☛ New_Study:_No,_Of_Course_Russian_Twitter_Trolls
                  Didn’t_Impact_The_2016_Election⠀⇛


                       Right after the 2016 election that saw Donald Trump
                       elected President, there was this collective wail
                       among many who were unable to comprehend how this
                       could have happened, searching for someone to
                       blame. Two targets quickly emerged: social media
                       and Russia. Often the two were combined into
                       “Russian trolls on social media.” As we’ve noted,
                       those Russian trolls certainly existed, and
                       certainly were trying to influence the election,
                       but it seemed dubious to us that they had any real
                       effect. As we noted the day after the election, it
                       was silly to claim that social media magically made
                       people vote for Trump.


                # ⚓ Scheerpost ☛ Walking_Back_the_Russian_Troll_Scare⠀⇛


                       None of the news outlets that helped spread
                       suspicion about Russian Twitter trolls helping
                       Trump win the 2016 U.S. election is owning up to
                       their hype or catching any flak.


                # ⚓ Techdirt ☛ The_Anti-Twitter_Files:_January_6th_Committee
                  Report_Shows_How_Twitter_Leaned_Over_Backwards_To_Protect
                  Trump_&_Conservatives⠀⇛


                       For all the talk of the “Twitter Files,” as we’ve
                       detailed, they’ve mostly been, at best, misleading,
                       and frequently actively wrong. One of the big
                       reveals, we were told, was that the Files were
                       going to expose the political machinations of how
                       Twitter banned former President Trump. And, indeed,
                       Bari Weiss’s “Part Five” of the Twitter Files, back
                       in mid-December, purported to reveal the big secret
                       reckoning. But if you haven’t heard much about it
                       since then, it’s because… they were a complete flop
                       when it came to anything of interest. Basically, it
                       was exactly what some of us said the day it
                       happened: a difficult decision with a number of
                       competing factors going into it. One that could
                       have gone either way, but recognizing the gravity
                       of what happened on January 6th, and the genuine
                       concern that Trump would continue to whip his fans
                       into an insurrectionist frenzy, one that you can
                       see a reasonable argument for making.


          o § Privacy/Surveillance⠀➾


                # ⚓ FAIR ☛ NYT_Worries_Big_Brother_Is_Not_Watching_You⠀⇛


                       A recent guest essay in the New York Times (12/28/
                       22) concluded a searing takedown of “our technology
                       overlords” with the sentence:


    * § Defence/Aggression⠀➾


          o ⚓ Meduza ☛ Russian_Defense_Ministry_says_Soledar_under_Russian
            control_—_Meduza⠀⇛


                 According to the Russian Defense Ministry’s daily
                 briefing, the Russian military has established full
                 control over the town of Soledar. The town has seen
                 fierce fighting over the last few weeks.


          o ⚓ Meduza ☛ After_Soledar_With_the_capture_of_a_Ukrainian_mining
            town,_Evgeny_Prigozhin’s_Wagner_Group_has_a_fine_prize_for_Putin.
            But_what’s_next?_—_Meduza⠀⇛


                 With the Russian army’s recently intensified offensive
                 toward Bakhmut, the city (together with the adjacent
                 salt-mining town of Soledar, whose name translates as
                 “salt giver”) emerged as Russia’s main objective in the
                 Donbas. On January 8, right after a 36-hour “ceasefire”
                 announced unilaterally by Russia but observed by no one,
                 Ukrainian President Volodymyr Zelensky spoke of the area
                 around Bakhmut as “one of the bloodiest places on the
                 frontline.” The following day, the Wagner Group launched
                 a “powerful assault” on Soledar itself, where Russian
                 troops were “literally advancing over their own soldiers’
                 dead bodies,” in the words of Ukrainian Deputy Defense
                 Minister Hanna Maliar. As of January 12, Wagner
                 detachments seemed to have seized the greater part of
                 Soledar — Prigozhin claiming sole credit for the Wagner
                 Group, while Russia’s Defense Ministry kept conspicuously
                 silent about the operation. The offensive itself,
                 meanwhile, still eludes full rational explanation, like
                 much else in Russian military strategy. Meduza’s podcast
                 host Vladislav Gorin and military analyst Dmitry Kuznets
                 tried to make sense of the Bakhmut offensive and its
                 place in the war’s big picture. Anna Razumnaya recaps how
                 Dmitry Kuznets understands the military situation and
                 what it foreshadows for the next phase of the war.


          o ⚓ Common Dreams ☛ How_Safe_Can_We_Really_Be_in_a_Nation_Such_as
            This?⠀⇛


                 It was the guacamole’s fault!


          o ⚓ Meduza ☛ Phishing_scam_invites_Russian_Telegram_users_to_check
            ‘conscription_lists’_to_see_if_they’ll_be_drafted_in_February_—
            Meduza⠀⇛


                 Russian Telegram users were targeted by a mass mailing of
                 malicious messages inviting them to view a list of people
                 allegedly pre-registered for enlisting in the Russian
                 army on February 1–3, 2023. This was reported by
                 In2Security, a Russian Telegram channel covering
                 information security.


          o ⚓ Meduza ☛ Russian_airline_regulator_tells_airlines_to_keep_crew
            members_from_swearing_on_intercom_—_Meduza⠀⇛


                 The Russian federal airline regulator Rosaviatsia has
                 instructed airlines to keep pilots and crew members from
                 using obscenities while on the aircraft intercom. The
                 regulator’s letter to Russian airlines prompted doubts
                 about the officials’ industry competence.


          o ⚓ Meduza ☛ Actor_Artur_Smolyaninov_and_others_declared_‘foreign
            agents’_—_Meduza⠀⇛


                 The Russian Ministry of Justice has expanded its list of
                 “foreign agents.”


          o ⚓ Scheerpost ☛ What_It_Means_for_Hunger_to_Burn_Through_the
            Pentagon’s_Ranks⠀⇛


                 Andrea Mazzarino describes in all-too-devastating detail
                 that the over-funded military-industrial complex is
                 stealing from the hungry.


          o ⚓ Scheerpost ☛ The_Winds_of_the_New_Cold_War_Are_Howling_in_the
            Arctic_Circle⠀⇛


                 With members of the Arctic Council refusing to work with
                 Russia since the start of the Ukraine War, the future of
                 the Arctic and its indigenous inhabitants (who are most
                 affected by climate change and mining interests) is at
                 stake. Geopolitical tensions in the region began more
                 than a decade ago when Arctic Council states began to
                 jockey for control over the area, not to stem the dangers
                 of climate change, but to exploit minerals, metals, and
                 fossil fuels within the Arctic Circle.


          o ⚓ Scheerpost ☛ Israel_Fascist?⠀⇛


                 Israel’s sharp turn to the extreme right has startled
                 American Jews.


          o ⚓ Scheerpost ☛ A_Pentagon_Report_on_China_Fuels_a_Military_Spending
            Frenzy_in_the_US⠀⇛


                 How the media is misrepresenting what’s in the document.


          o ⚓ The Nation ☛ An_Appeals_Court_Wants_to_Bring_Back_Bump_Stocks,
            Beloved_by_Mass_Shooters⠀⇛


                 The conservative judges who now occupy large swaths of
                 the federal judiciary are pro-gun extremists. They’re so
                 deep in the thrall of the gun lobby that their anti-
                 regulatory opinions are now incompatible with mainstream
                 American views on gun safety. Conservative judges have
                 even lurched to the right of the Republican presidents
                 who appoint them. The proof of that came this week when
                 the hyper-conservative US Court of Appeals for the Fifth
                 Circuit threw out a Trump-era gun safety rule. The
                 culture of violence embraced by these Federalist
                 Society–approved judges is a greater threat to peace and
                 personal safety than all the violent video games and
                 Hollywood movies could ever be.1


          o ⚓ The Nation ☛ The_Failures_of_the_January_6_Report⠀⇛


                 The American government has developed a unique ritual for
                 healing national traumas: the convening of investigatory
                 commissions tasked with assembling thick tomes to explain
                 why bad things happen to good nations. This was the
                 response after the race riots of 1919, the Japanese
                 attack on Pearl Harbor, President Kennedy’s
                 assassination, the race riots of the 1960s, 9/11, and
                 other collective tragedies.


    * § Transparency/Investigative Reporting⠀➾


          o ⚓ The Dissenter ☛ CIA_Pushes_For_Dismissal_Of_Lawsuit_Against
            Alleged_Spying_On_Assange_Visitors⠀⇛


    * § Environment⠀➾


          o ⚓ The Nation ☛ Biggest_Carbon_Footprint⠀⇛


          o § Energy/Transportation⠀➾


                # ⚓ Zimbabwe ☛ Zimbabwe’s_unreliable_electricity_supply_makes
                  it_the_biggest_adopter_of_solar_systems_in_Africa⠀⇛


                       In a survey done of 34 African countries, only 43%
                       of households enjoyed an electricity supply that is
                       available all the time or most of the time. Only 4
                       countries in Africa enjoy 100% availability of
                       electricity and these are Egypt, Algeria, Morocco,
                       and Tunisia. As for the survey, of those 34
                       countries, Zimbabweans are the biggest adopter of
                       solar for backup electricity as a percentage of the
                       total number of households.


                # ⚓ Common Dreams ☛ Staff_at_Zaporizhzhia_Nuclear_Plant_in_War-
                  Torn_Ukraine_Awarded_for_Heroism⠀⇛


                       A U.S.-based group on Friday recognized the
                       “heroic” Ukrainian staff at a Russian-controlled
                       nuclear power plant, highlighting concerns about
                       the facility nearly 11 months into Russia’s
                       invasion.


                # ⚓ Common Dreams ☛ NY_Agency_Sued_Over_Cryptomining_Operation
                  That_Could_Increase_Emissions_by_3,500%⠀⇛


                       Three climate action groups said Friday that New
                       York’s decision to allow a Canadian cryptocurrency
                       mining company to control a fracked gas power plant
                       is a clear violation of the state’s landmark
                       climate protection law as they sued a state
                       commission in Albany County Supreme Court.


                # ⚓ Common Dreams ☛ ‘This_Is_Corruption’:_Manchin_Chief_of
                  Staff_Now_Chief_Lobbyist_for_Big_Oil⠀⇛


                       The top aide of Sen. Joe Manchin, a close ally of
                       the fossil fuel industry, is leaving the West
                       Virginia Democrat’s office to work directly for Big
                       Oil as a lobbyist at the American Petroleum
                       Institute, one of the most powerful influence-
                       peddling organizations in the United States.


                # ⚓ Hackaday ☛ Increasing_PV_Solar_Cell_Efficiency_Through
                  Cooling⠀⇛


                       An unavoidable aspect of photovoltaic (PV) solar
                       panels is that they become less efficient when they
                       warm up. [Tech Ingredients] explains in a new video
                       the basic reason for this, which involves the input
                       of thermal energy affecting the semiconductor
                       material. In the subsequent experiment, it is
                       demonstrated how cooling the backside of the panel
                       affects the panel’s power output.


                # ⚓ TruthOut ☛ Manchin’s_Chief_of_Staff_to_Become_Top_Lobbyist
                  at_American_Petroleum_Institute⠀⇛


    * § Finance⠀➾


          o ⚓ Common Dreams ☛ As_Debt_Ceiling_Alarm_Sounded,_GOP_Accused_of
            Plotting_‘Terrorist_Attack_on_the_Economy’⠀⇛


                 As Treasury Secretary Janet Yellen warned Friday that the
                 United States is likely to reach its arbitrary borrowing
                 limit next week, progressives denounced congressional
                 Republicans for threatening to use a debt ceiling
                 standoff to force cuts to popular federal programs
                 including Medicare and Social Security.


          o ⚓ Common Dreams ☛ New_GAO_Report_Confirms_Trump_Tax_Cuts_Were
            Massive_Corporate_Giveaway⠀⇛


                 The tax cuts signed into law by former President Trump at
                 the end of 2017 were a boon for profitable corporations,
                 according to a new report released by the Government
                 Accountability Office. It finds the average effective
                 federal income tax rate paid by large, profitable
                 corporations fell to 9 percent in the first year that the
                 Trump tax law was in effect, and the share of such
                 companies paying nothing at all rose to 34 percent that
                 year.


          o ⚓ Common Dreams ☛ 34%_of_Big,_Profitable_US_Corporations_Paid_$0_in
            Federal_Taxes_in_1st_Year_of_Trump_Tax_Law⠀⇛


                 A study released Friday by the Government Accountability
                 Office found that more than a third of large, profitable
                 corporations in the United States paid nothing in federal
                 income taxes in 2018, the year the regressive Trump-GOP
                 tax cuts took effect.


          o ⚓ The Nation ☛ How_Student_Loan_Cancellation_Helps_Asian
            Americans⠀⇛


                 When policy-makers and advocates talk about uplifting
                 minority communities, the concerns of Asian American and
                 Pacific Islander communities are often left out of the
                 discussion—especially when critiquing our current student
                 debt system. Part of this can be tied to the “model
                 minority” myth—a harmful stereotype that assumes
                 widespread socioeconomic success and high achievements
                 for the AAPI population.


          o ⚓ TruthOut ☛ Watchdog_Calls_for_Investigation_Into_IRS_Over
            Repeated_Failure_to_Audit_Trump⠀⇛


    * § AstroTurf/Lobbying/Politics⠀➾


          o ⚓ Common Dreams ☛ GOP-Led_Missouri_House_Strips_Women_Lawmakers_of
            ‘Right_to_Bare_Arms’_With_New_Dress_Code⠀⇛


                 Missouri state lawmakers can bear arms in the legislative
                 chamber but if they’re women, they can no longer show
                 their bare arms under new dress code rules passed by the
                 Republican-controlled House of Representatives on Friday.


          o ⚓ The Nation ☛ Postcard_From_the_Edge⠀⇛


          o ⚓ Reason ☛ Did_‘Every_Conspiracy_Theory’_About_Twitter_Turn_Out_To
            Be_True?⠀⇛


                 Twitter began transparently labeling accounts associated
                 with any government, whether it be a politician or a
                 state-run media outlet. It also pledged to Congress to
                 “rapidly identify and shut down all state-backed covert
                 information operations & deceptive propaganda.”


          o ⚓ AntiWar ☛ Former_High-Level_US_Officials_Warn_Time_Is_Not_on
            Ukraine’s_Side_in_the_Conflict_–_News_From_Antiwar.com⠀⇛


                 Former US Secretary of State Condoleezza Rice and former
                 Secretary of Defense Robert Gates warned in an op-ed
                 published by The Washington Post on Saturday that “time
                 is not on Ukraine’s side” as its economy is in shambles
                 and the country is entirely reliant on foreign aid.


          o ⚓ Michael West Media ☛ Dominic_Perrottet’s_Nazi_uniform_brings
            tears_to_the_pokies_lobby_…_tears_of_joy_–_Michael_West⠀⇛


                 Dominic Perrottet’s Nazi uniform prank is good news for
                 ClubsNSW and the pokies lobby. The NSW Premier had held
                 firm on a cashless gaming card but now is fighting for
                 his political life.


          o ⚓ Common Dreams ☛ House_GOP_Scraps_Consumer_Protection_Panels_in
            ‘First_of_Many_Gifts’_to_Wall_Street⠀⇛


                 The U.S. committee tasked with overseeing the financial
                 sector on Thursday “dispelled any doubt of their intent
                 to do the bidding of the financial industries over the
                 interests of everyday families,” said a government
                 watchdog group as the panel signaled it will
                 significantly scale back its efforts to push for consumer
                 protections on Wall Street.


          o ⚓ Common Dreams ☛ Trump_Organization_Ordered_to_Pay_Maximum_Penalty
            of_$1.6M_for_Fraud⠀⇛


                 A New York Supreme Court judge on Friday ordered the
                 Trump Organization, former President Donald Trump’s real
                 estate empire to pay the maximum criminal penalty for
                 charges including tax fraud.


          o ⚓ TruthOut ☛ Trump_Organization_Hit_With_Maximum_Fine_of_$1.6
            Million_for_Tax_Evasion_Scheme⠀⇛


          o ⚓ Common Dreams ☛ Peruvians_Tell_Unelected_President_to_‘Stop_This
            Massacre,’_Resign_Immediately⠀⇛


                 Thousands of people hit the streets of Peru’s capital
                 Lima on Thursday in a peaceful protest against the
                 national government, which has been led for over a month
                 by unelected President Dina Boluarte.


          o ⚓ Common Dreams ☛ Fortress_Europe_Is_Cruel,_Misguided,_and_Doomed
            to_Fail⠀⇛


                 It’s time to rethink EU migration policy. New walls are
                 being built in Europe, but they will not solve the
                 present crisis – and the money could be far better spent.


          o ⚓ TruthOut ☛ 24_People_Face_Trial_for_Giving_Life-Saving_Assistance
            to_Migrants_in_Europe⠀⇛


          o ⚓ Democracy Now ☛ The_Crisis_of_Missing_Migrants:_Tens_of_Thousands
            of_People_Have_Disappeared_on_Their_Way_to_Europe⠀⇛


                 Twenty-four volunteer rescue workers connected to the
                 group Emergency Response Centre International face trial
                 for human smuggling in Greece for giving life-saving
                 assistance to thousands of migrants, mostly from sub-
                 Saharan Africa and the Middle East, fleeing violence,
                 poverty and persecution. A European Parliament report
                 described the trial as Europe’s “largest case of
                 criminalization of solidarity.” We’re joined by New
                 Yorker staff writer Alexis Okeowo. Their latest piece,
                 “The Crisis of Missing Migrants,” covers the migrant
                 crisis in the Mediterranean and the tens of thousands of
                 people who have gone missing en route to Europe. “It’s so
                 inhumane, the way people are being forced to cross to
                 Europe. And that is, by the way, because there are not
                 safer migrant crossings. There are not more open migrant
                 routes. We are forcing migrants to do this,” Okeowo says.


          o ⚓ Common Dreams ☛ GOP_Destruction_of_House_Ethics_Committee_Tells
            You_Everything_You_Need_to_Know⠀⇛


                 They came to Washington last week ready to represent the
                 constituents who had given them the honor of serving in
                 Congress. They were 39 freshman Republican House Members.


          o ⚓ Scheerpost ☛ In_Biden_Documents_Story,_Stenography_and_Scandal
            Take_Center_Stage⠀⇛


                 Many outlets focused on what each party had to say about
                 the story—rather than what the general public ought to
                 understand about it.


          o ⚓ Democracy Now ☛ Legendary_Prosecutor_Luis_Moreno_Ocampo_on
            “Argentina,_1985”_and_Why_Democracy_Is_at_Risk_Today⠀⇛


                 Former Argentine prosecutor Luis Moreno Ocampo, who
                 served as deputy prosecutor in Argentina’s Trial of the
                 Juntas and later as the first prosecutor of the
                 International Criminal Court, is portrayed in the film
                 “Argentina, 1985,” which won the Golden Globe for Best
                 Motion Picture in a Non-English Language this week. The
                 film dramatizes the efforts of Argentina’s civilian court
                 to prosecute the country’s former military leaders for
                 brutal crimes committed during the U.S.-backed right-wing
                 military dictatorship from 1976 to 1983. Ocampo spoke to
                 Democracy Now! recently about that landmark trial, the
                 new film and why “democracy is at risk everywhere.”


          o ⚓ Democracy Now ☛ “Argentina,_1985”:_Oscar-Shortlisted_Film_Depicts
            Historic_War_Crimes_Trial_of_U.S.-Backed_Generals⠀⇛


                 We speak with director Santiago Mitre about “Argentina,
                 1985,” his dramatization of the Trial of the Juntas, when
                 a civilian court prosecuted Argentina’s former military
                 leaders for brutal crimes committed during the U.S.-
                 backed right-wing military dictatorship from 1976 to
                 1983. The film just won a Golden Globe for Best Motion
                 Picture in a Non-English Language and is also shortlisted
                 for an Oscar for best international film. Mitre talks
                 about following the landmark trial in Argentina as a boy,
                 just a short time after the end of the dictatorship, and
                 why he felt compelled to tell the story as a filmmaker.
                 “The decision of the government to do this trial was very
                 brave and very important, and it founded the basis of the
                 new democracy,” says Mitre.


          o ⚓ Counter Punch ☛ Fiery_Flying_Roll⠀⇛


                 Bad luck on Friday the thirteenth, at least in 1650,
                 because on that day, 13 January 1650, Abiezer Coppe was
                 transferred from a prison in Warwick to one in Coventry
                 and then some time later to London and Newgate
                 prison.  Coppe was imprisoned for “putting forth,” or
                 publishing, A Fiery Flying Roll: A Word from the Lord to
                 all the Great Ones of the Earth.


                 It was a revolutionary time.  Less than a year earlier,
                 30 January 1649, the King, Charles I, was decapitated,
                 and shortly thereafter Parliament replaced monarchy with
                 a commonwealth.  This put an end to the divine right of
                 kings.  At the same time the Levellers with their
                 principle of political equality and the Diggers with
                 their principle of  commoning land were defeated.  These
                 defeats cleared the way forward for capitalist conditions
                 of exploitation by the thorough separation of workers
                 from the means of production, especially land.  Slavery
                 or prison became the future.


          o ⚓ The Nation ☛ Will_This_Be_the_Year_Dianne_Feinstein_Finally
            Retires?⠀⇛


    * § Censorship/Free Speech⠀➾


          o ⚓ Computer World ☛ Google_warns_court_against_changing_liability
            shield_for_[Internet]_companies⠀⇛


                 In a defense brief filed to the US Supreme Court
                 Thursday, Google warned that altering Section 230 of the
                 Communications Decency Act — which protects internet-
                 based companies from being sued for content created by
                 their users — would “upend the [Internet].”


                 [...]


                 The Gonzalez family argues that the algorithms that
                 Google and YouTube use to target certain content to users
                 are the creations of the companies themselves, not users
                 or other third parties, and as such are essentially
                 editorial functions for which they are responsible — and
                 so the algorithms are not protected by Section 230.


          o ⚓ Idiomdrottning ☛ NATO_vs_Erdoğan⠀⇛


                 The Erdoğan dictatorship wants Sweden to ban completely
                 normal things such as protests and journalism.


          o ⚓ BIA Net ☛ Verdict_for_Şansal_for_‘insulting_President_with
            Gollum’_overturned_by_Regional_Court⠀⇛


                 The 2nd Penal Chamber of the Istanbul Regional Court of
                 Justice has overturned a prison sentence for Barbaros
                 Şansal. In the previous sentence, Şansal was convicted to
                 one year and two months in prison for retweeting a photo
                 comparing President Erdoğan to Lord Of The Rings
                 character Gollum.


                 The regional court has overturned the decision for Şansal
                 as there are pending case files about the defendant for
                 the same crime.


          o ⚓ NPR ☛ In_‘No_Bears’,_a_banned_filmmaker_takes_bold_aim_at_Iranian
            society⠀⇛


                 It’s a brilliant movie — an intricate and layered drama
                 that somehow manages to be funny, angry, playful and
                 despairing by turns. Panahi is as incisive a social
                 critic as ever, and here he targets the misogyny and
                 religious fundamentalism that hold sway across Iran —
                 issues that led to the violent unrest currently gripping
                 the country.


          o ⚓ Techdirt ☛ Internet_Safe_Harbors,_Antisemitism,_And_Online_Jewish
            Activity⠀⇛


                 In early December 2022, a former Israeli Minister of
                 Defense and Chief of Staff of the Israel Defense Forces,
                 three other retired Israeli generals, a former
                 Commissioner of the Israeli Police, and a former head of
                 the Mossad’s Intelligence Directorate filed an amicus
                 brief before the U.S. Supreme Court in Gonzalez v.
                 Google arguing that Internet platforms should be civilly
                 liable for third party content that encourages terrorist
                 activity. In their filing, they claimed that the wave of
                 terror in Israel in 2015–2016 “became known as the
                 ‘Facebook intifada’ and the #stab! Campaign due to the
                 essential role social media played in inciting the
                 perpetrators to attack civilians.” The Anti-Defamation
                 League also filed a brief in the case, similarly arguing
                 that Internet platforms should have legal accountability
                 for violence against Jewish Americans and other
                 vulnerable communities encouraged by these platforms’
                 recommendation engines. So, too, the Zionist Organization
                 of America asserted that Internet platforms should not be
                 immune from liability “when they target specific users
                 and recommend and direct them to new content that helps
                 fan the flames of hatred and violence against the Jewish
                 community.”


          o ⚓ Techdirt ☛ Appeals_Court_Judge_Suggests_Hate_Speech_Shouldn’t_Be
            Protected_In_Decision_Against_Students_Expelled_For_Bigoted_Social
            Media_Posts⠀⇛


                 Last year, the Supreme Court handed down a ruling in a
                 school free speech case that came down squarely, if very
                 narrowly, on the side of the student. The student suing
                 over being kicked off the cheerleading squad for sending
                 a snapchat message saying “fuck school fuck softball fuck
                 cheer fuck everything” prevailed, with the nation’s top
                 court finding her speech, however crude, was protected by
                 the First Amendment.


    * § Freedom of Information / Freedom of the Press⠀➾


          o ⚓ FAIR ☛ David_Sirota_on_Accountability_Journalism⠀⇛


                  


    * § Civil Rights/Policing⠀➾


          o ⚓ ‘The_government_killed_him’:_A_tribute_to_activist_and_programmer
            Aaron_Swartz_10_years_after_his_death⠀⇛


                 As a computer programmer, Swartz changed the internet
                 forever and fiercely fought against the privatization of
                 knowledge. The federal government persecuted him for it
                 until his death by suicide in 2013.


          o ⚓ Common Dreams ☛ Labor,_Rights_Groups_Praise_Biden_Policy_Boosting
            Migrant_Worker_Protections⠀⇛


                 Migrant workers and advocates on Friday applauded a Biden
                 administration policy to help protect noncitizen
                 employees who are victims or witnesses of labor rights
                 violations “from threats of immigration-related
                 retaliation from the exploitive employers.”


          o ⚓ NPR ☛ Many_workers_barely_recall_signing_noncompetes,_until_they
            try_to_change_jobs⠀⇛


                 Researchers estimate that one in five workers in the U.S.
                 — some 30 million people — have signed noncompete
                 agreements, prohibiting them from taking jobs at similar
                 businesses or starting a rival business of their own
                 within a certain time period, typically six months to two
                 years.


          o ⚓ VOA News ☛ After_132_Years,_Wounded_Knee_Artifacts_Come_Home⠀⇛


                 Part 1 of this series looked at the circumstances leading
                 to a massacre of Lakota men, women and children at
                 Wounded Knee, South Dakota, on December 29, 1890. In
                 November, a museum in Barre, Massachusetts, repatriated
                 more than 150 objects believed to have been looted from
                 the massacre site. VOA dug through historic records and
                 archives to trace how and when they were obtained, how
                 they made their way to New England, and more than a
                 century later, back to the Lakota.


          o ⚓ VOA News ☛ Lakota_Descendants_Remember_Ancestors_Killed_at
            Wounded_Knee⠀⇛


                 In the Treaty of Fort Laramie in 1868, the U.S.
                 government set aside 233,000 square kilometers west of
                 the Missouri River for the “absolute and undisturbed use
                 and occupation” of the Lakota, Dakota and Nakota tribes,
                 collectively known as the Sioux.


                 When Lieutenant General George Custer and his 7th Cavalry
                 confirmed there was gold in the Black Hills of that area,
                 prospectors rushed in. By 1875, the Bureau of Indian
                 Affairs ordered the tribes to move. When they resisted,
                 the U.S. government sent in troops, setting off armed
                 conflict that would see Custer defeated.


          o ⚓ RTL ☛ Iran_executes_British-Iranian_dual_national_for_spying⠀⇛


                 BBC Persian on Wednesday aired an audio message it said
                 was from Akbari in which he said he was tortured and
                 forced to confess on camera to crimes he did not commit.


          o ⚓ BBC ☛ Alireza_Akbari:_Iran_executes_British-Iranian_dual
            national⠀⇛


                 Mr Akbari alleged that he was “interrogated and tortured”
                 by intelligence agents “for more than 3,500 hours”.


          o ⚓ Common Dreams ☛ ‘They’re_Trying_to_George_Floyd_Me’:_Teacher_and
            Cousin_of_Black_Lives_Matter_Co-Founder_Killed_by_LAPD⠀⇛


                 Harrowing video footage released this week shows officers
                 with the Los Angeles Police Department forcibly
                 restraining and repeatedly using a Taser on 31-year-old
                 Keenan Anderson—a high school teacher and cousin of Black
                 Lives Matter co-founder Patrisse Cullors—following a
                 traffic accident.


          o ⚓ TruthOut ☛ Keenan_Anderson,_Cousin_of_Black_Lives_Matter
            Cofounder,_Killed_by_LAPD⠀⇛


          o ⚓ TruthOut ☛ The_Supreme_Court_Is_About_to_Eviscerate_the_Right_to
            Strike⠀⇛


          o ⚓ Internet Freedom Foundation ☛ Civil_Society’s_second_opinion_on_a
            UHI_prescription⠀⇛


                 The National Health Authority (NHA) released the
                 Consultation Paper on Operationalising Unified Health
                 Interface (UHI) in India on December 14, 2022. The
                 deadline for submission of comments was January 13, 2023.
                 We collaborated with the Centre for Health Equity, Law &
                 Policy, the Centre for Internet & Society, & the Forum
                 for Medical Ethics Society to submit comments on the
                 paper.


    * § Internet Policy/Net Neutrality⠀➾


          o ⚓ Techdirt ☛ Senators_Say_The_FCC’s_New_Maps_Still_Suck,_Overstate
            Coverage⠀⇛


                 We’ve noted more than a few times that U.S. taxpayers
                 have spent nearly $400 million on mapping U.S. broadband,
                 yet the FCC still somehow routinely produces maps that
                 greatly overstate broadband coverage, and greatly
                 understate the obvious impact of monopolization and
                 stunted broadband competition.


          o ⚓ Joe Brockmeier ☛ Laws_of_technology_and_remote_work_:_Dissociated
            Press⠀⇛


                 A laptop’s cabling will always be located on the
                 maximally inconvenient side. Especially power cords with
                 bulky connectors.


                 [...]


                 After troubleshooting a system or application extensively
                 it will turn out that the problem is a faulty cable or
                 coincidental internet glitch. However, you are likely to
                 have introduced a new, unrelated problem in an attempt to
                 fix the symptoms.


    * § Digital Restrictions (DRM)⠀➾


          o ⚓ Video ☛ The_DRM_Future_of_Subscription_Based_Cars⠀⇛


                 In this video I discuss the growing subscription based
                 model of motor vehicles where people are having to pay an
                 additional monthly fee or large one time fee to unlock
                 heated seats or heated steering wheels when these
                 features already exist in the cars.


    * § Monopolies⠀➾


          o § Trademarks⠀➾


                # ⚓ Techdirt ☛ Luka_Doncic’s_Trademark_Dispute_With_His_Mother
                  Settles⠀⇛


                       Over the summer, we discussed what looked to be a
                       fascinating trademark dispute between NBA superstar
                       Luka Doncic and his mother, Mirjam Poterbin. As a
                       quick summary, Doncic consented to have trademarks
                       referring to him registered to his mother, as he’d
                       become a star overseas at age 13. That itself isn’t
                       all that odd. But now Doncic has his own company
                       managing his name and likeness rights, Luka77,
                       which applied for trademarks at Doncic’s request,
                       only to have them refused as being too similar to
                       the marks held by Poterbin. From there, Luka77
                       petitioned the USPTO to cancel Poterbin’s marks,
                       with Doncic asserting he no longer wanted his
                       mother to control them.


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ RIAA’s_Pirate_Domain_Name_Policing_Efforts
                  Are_Unspectacular⠀⇛


                       The RIAA is designated as a “trusted notifier” by
                       domain name registry operator Identity Digital,
                       which oversees hundreds of TLDs. The partnership
                       allows the music group to flag piracy domains, but
                       transparency reports show absolutely no recent
                       activity on this front.


                # ⚓ Torrent Freak ☛ Four_Genshin_Impact_Leakers_Targeted_in_New
                  Set_of_DMCA_Subpoenas⠀⇛


                       After targeting Ubatcha, one of the most popular
                       and prolific Genshin Impact leakers, publisher
                       Cognosphere has several new targets on its radar.
                       DMCA subpoena applications obtained by TorrentFreak
                       reveal that users of the popular ‘House of Daena’
                       Discord channel are among the targets


                # ⚓ BBC ☛ Creedence_Clearwater_Revival’s_John_Fogerty_wins
                  music_rights⠀⇛


                       Following a 50-year legal battle, the founding
                       member of Creedence Clearwater Revival now owns the
                       global publishing rights to the iconic rock band’s
                       songs.


                       It came after Mr Fogerty, 77, bought a majority
                       stake in the rights to the band’s catalogue from
                       Concord Records, which has owned the rights since
                       2004.


                       “As of January this year, I own my own songs
                       again,” he wrote on Twitter.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ 🔤SpellBinding:_AEHIRYW_Wordo:_AMITY⠀⇛


          o § Technical⠀➾


                # ⚓ Free_software_worth_checking_out._Vol._II⠀⇛


                       It’s been two years since the first “Free software
                       worth checking out,” can you believe it? Well, I’ve
                       had two years to discover new cool stuff, so here’s
                       what I can sell. There’s a lot of cool free (as in
                       freedom) software out there!


                # ⚓ RE:_DNS_oddity⠀⇛


                       Saw JBanana’s gemlog yesterday about a weird
                       phenomenon with DNS. Namely in the logs, the IP
                       address 127.0.0.1 got logs as some Brazillian
                       domain name. And the resolver runs in a NAT so no
                       external entity could access it. Thus there mush be
                       some issue somewhere.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.



                    ䷩ 𝚕𝚒𝚗𝚎 6111

╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.14.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_14/01/2023:_KDE_Frameworks_5.102.0_and_Mesa_23_RC⠀✐


Posted in News_Roundup at 7:32 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Reviews
          o Red_Hat
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o GNU_Projects
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Science
          o Security
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o ⚓ Veira_Group_introduces_Linux-based_Coolita_2.0_solutions_for_the
            Indian_Smart_TV_market._–_Newspatrolling.com⠀⇛


                 Veira Group, one of India’s largest ODM for Smart TVs
                 introduces Linux-based Coolita 2.0 solutions for the
                 country’s growing smart TV market. With this development,
                 Veira Group enters a new tech territory in partnership
                 with the proprietary Coolita OS, highlighting its
                 commitment to building a new smart TV ecosystem. Coolita
                 OS is Skyworth first self-developed smart TV operating
                 system, delivering a lighter, smoother, more convenient
                 user experience.


                 With the release of the Coolita 2.0 solutions, Veira
                 intends to sell 500,000 Smart TVs equipped with the new
                 OS for the top Indian brands. The new OS is set to
                 transform the smart TV experience, for today’s internet-
                 driven generation. It offers a wide variety of
                 entertainment options and applications, such as YouTube,
                 Prime Video, Zee5, Hungama, SonyLiv Etc. with a range of
                 global and local content. Other features of this lite TV
                 OS include pre-installed lite cloud games, a built-in
                 Internet browser, an app store and a Data Saver that
                 provides real-time data reminders to help people
                 efficiently manage their data usage. Any Smart TV device
                 that is connected to LAN can be used to watch a movie
                 with network-free screen projection. With an exceptional
                 user experience, platform stability, and affordability,
                 Coolita is expected to become one of the leading &
                 preferred Smart TV OS’s in India.


          o ⚓ Veira_Group_introduces_Linux-based_Coolita_2.0_solutions_for_the
            Indian_Smart_TV_market_–_Content_Media_Solution⠀⇛


          o ⚓ Make Use Of ☛ The_9_Best_Career_Options_After_Learning_Linux⠀⇛


                 Ready to start your professional Linux career? Here are
                 some of the best job options for you after you’ve learned
                 Linux and open source.


                 There is a reason why many people use Linux but in
                 different capacities. From using Linux distros as
                 individual users to developers writing apps for Linux
                 users, there is a different purpose associated with
                 Linux.


                 When working on Linux, you can pursue various career
                 options and avenues. Each stream will open opportunities,
                 allowing you to make the most out of your newly derived
                 skills.


                 You can pursue a few options after getting familiar with
                 Linux and its related technologies. Here are a few top
                 professions you can choose after learning Linux.


          o ⚓ Linux Links ☛ Linux_Around_The_World:_USA_–_Missouri_–
            LinuxLinks⠀⇛


                 We cover events and user groups that are running in the
                 US state of Missouri. This article forms part of our
                 Linux Around The World series.


          o § Desktop/Laptop⠀➾


                # ⚓ Notebook Check ☛ System76_teases_beefy_Pangolin_Linux
                  laptop_update_with_Ryzen_7_6800U_–_NotebookCheck.net_News⠀⇛


                       System76 is known for its high-quality laptops that
                       run Linux (either Ubuntu or System76′s own
                       Pop!_OS). However, most of their laptops run on
                       Intel CPUs, so AMD fans were left in the lurch…
                       until the original Pangolin debuted a few years
                       ago. System76 recently teased the upcoming version
                       of the Pangolin, replete with the latest and
                       greatest from AMD.


                       The new Pangolin will come with AMD’s Ryzen 7 6800U
                       CPU, Radeon 680M integrated graphics (built on
                       AMD’s RDNA 2 architecture), and up to 32 GB of
                       LPDDR5 RAM (6400 MHz). The laptop will have slots
                       for two M.2 PCIe NVMe SSDs (up to 16 TB total).


                       Connectivity is covered by three USB-A 3.2 Gen 1 (5
                       Gbps) ports, a single USB-C 3.2 Gen 2 (10 Gbps)
                       port, and an SD card reader. USB 4 is noticeably
                       absent. An HDMI 2.0 port and 3.5 mm combo audio
                       jack round out connections.


                       The Pangolin has most of the conveniences of other
                       modern laptops, including a backlit chiclet-style
                       keyboard, a multitouch trackpad, and a Kensington
                       lock. The webcam falls flat at only 1 MP (720p),
                       but there is a hardware kill switch to turn off the
                       webcam.


          o § Audiocasts/Shows⠀➾


                # ⚓ My_podcast_tastes_|_AksDev⠀⇛


                       I just wanted to write this down since I’ve been
                       talking a bit about podcasts on fediverse.


                       I listen a lot of podcasts when gaming, it’s kind
                       of a way how I relax. Nothing like good multiplayer
                       FPS where I can turn off my brains, then I can
                       listen podcasts on the side. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:)⦈


                # ⚓ Video ☛ Don’t_Buy_An_AMD_7900_XT_–_XTX_On_Linux_–
                  Invidious⠀⇛


                       As always don’t buy a GPU on the launch of a new
                       architecture, and the RDNA 3 cards with the 7900 XT
                       and XTX prove that to be true again, these cards
                       are a mess on Linux right now.


                # ⚓ Video ☛ Should_I_Convert_Ext3_to_Ext4?_–_Invidious⠀⇛


                       Let me know what you think… Should I convert my /
                       partition from Ext3 to Ext4?


                # ⚓ mintCast Podcast ☛ 403_–_2023_Predictions_–_mintCast⠀⇛


                       Linux Mint 21.1 Vera released, Goodbye SHA-1: NIST
                       Retires 27-Year-Old Widely Used Cryptographic
                       Algorithm, Pine Tab2 announced, More developers
                       reportedly now use Linux than macOS


                # ⚓ Video ☛ Archcraft:_Minimal_Linux_Based_on_Arch_–
                  Invidious⠀⇛


                       Today we look at ArchCraft with the OpenBox window
                       manager and dig into the default settings. This
                       Linux distro is not user friendly, but is powerful
                       for those willing to learn it.


                # ⚓ Video ☛ Apple_spies_on_users,_Mastodon_loses_users,_Mozilla
                  ♥️_Fediverse:_Linux_–_Open_Source_News_–_Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Linux_6.1.6_[LWN.net]⠀⇛


                       I’m announcing the release of the 6.1.6 kernel.


                       All users of the 6.1 kernel series must upgrade.


                       The updated 6.1.y git tree can be found at:
                       git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-6.1.y
                       and can be browsed at the normal kernel.org git web
                       browser:


                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s…


                       thanks,


                       greg k-h


                # ⚓ LWN ☛ Linux_5.15.88_[LWN.net]⠀⇛


                       I’m announcing the release of the 5.15.88 kernel.


                       All users of the 5.15 kernel series must upgrade.


                       The updated 5.15.y git tree can be found at:
                       git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.15.y
                       and can be browsed at the normal kernel.org git web
                       browser:


                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s…


                       thanks,


                       greg k-h


                # ⚓ LWN ☛ Linux_5.10.163_[LWN.net]⠀⇛


                       I’m announcing the release of the 5.10.163 kernel.


                       All users of the 5.10 kernel series must upgrade.


                       The updated 5.10.y git tree can be found at:
                       git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.10.y
                       and can be browsed at the normal kernel.org git web
                       browser:


                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s…


                       thanks,


                       greg k-h


          o § Graphics Stack⠀➾


                # ⚓ Free Desktop ☛ [ANNOUNCE]_mesa_23.0.0-rc1⠀⇛


                       Hi list,

                       I'd like to announce mesa 23.0.0-rc1, which is now
                       available for general
                       consumption. The branch was made yesterday, as many
                       noticed, but I
                       wasn't able to get the actual relase cut until
                       today. There's a ton of
                       great changes here.

                       As always, please be sure to test and file issues
                       for any problems you
                       run into.

                       Cheers,
                       Dylan
          o § Applications⠀➾


                # ⚓ Ubuntu Handbook ☛ Kid3_Autio_Tagger_Celebrate_Its_20th
                  Birthday_by_Releasing_v3.9.3_|_UbuntuHandbook⠀⇛


                       Kid3, the free and open-source Qt app for editing
                       audio tags, now is 20 years old!


                       It was January 12, 2003, exactly 20 years ago, when
                       the first version 0.1 of Kid3 was released. And,
                       it’s the first app that I used to edit music tags
                       in Ubuntu when in 2008.


          o § Instructionals/Technical⠀➾


                # ⚓ UNIX Cop ☛ How_to_Install_Varnish_with_Apache_on_Ubuntu
                  22.04⠀⇛


                       . We already know that Apache is one of the best
                       web servers out there. But there are always tools
                       to improve it and to increase its power. So, today,
                       you will learn how to install Varnish with Apache
                       on Ubuntu 22.04.


                # ⚓ Kifarunix ☛ Perform_Unattended_VM_Installation_on
                  VirtualBox_7⠀⇛


                # ⚓ ID Root ☛ How_To_Install_uTorrent_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       uTorrent on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, µTorrent (also known as uTorrent) is a
                       popular and widely used BitTorrent client that
                       allows users to download and manage torrent files.
                       One of the key features of µTorrent is its small
                       size and minimal system requirements. It is
                       designed to be lightweight and fast, which makes it
                       suitable for use on older or less powerful
                       computers. It also has a simple and user-friendly
                       interface, which makes it easy to use for both
                       beginners and advanced users.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the uTorrent BitTorrent client on
                       Ubuntu 22.04 (Jammy Jellyfish). You can follow the
                       same instructions for Ubuntu 22.04 and any other
                       Debian-based distribution like Linux Mint,
                       Elementary OS, Pop!_OS, and more as well.


                # ⚓ AddictiveTips ☛ How_to_install_and_use_the_G4Music_app_on
                  Linux⠀⇛


                       If you’ve been looking for a new music app for
                       Linux, look no further than G4Music. G4Music is a
                       new, elegant GTK4 music application for Linux. It
                       is light and easy to use. In this guide, we’ll show
                       you how to install and use it on your Linux system.


                # ⚓ Red Hat Official ☛ Automating_HA_cluster_configuration_with
                  RHEL_system_roles⠀⇛


                       The ability to provide services to customers
                       continuously and with minimal-to-no outages is
                       critical in today’s world. The Red Hat Enterprise
                       Linux (RHEL) High Availability Add-On can help you
                       achieve that goal by improving the reliability,
                       scalability and availability of production systems.
                       High availability (HA) clusters do this by
                       eliminating single points of failure and by failing
                       over services from one cluster node to another in
                       case a node becomes inoperative.


                       In this post, I’ll demonstrate using the ha_cluster
                       RHEL system role to configure an HA cluster running
                       an Apache HTTP server with shared storage in
                       active/passive mode.


                # ⚓ Video ☛ Create_Your_Own_Emacs_Start_Page_–_Invidious⠀⇛


                       In the last few days, I have been playing around
                       with creating my own “start page” for Doom Emacs.
                       By default, Doom comes with its own “dashboard”
                       program but I wanted to create my own, mainly for
                       the experience, but also because I could create a
                       start page that was tailored exactly to my needs..


                # ⚓ How_to_enable_developer_mode_on_Chrome_OS_Flex⠀⇛


                       I have recently switched to Chrome OS Flex as main
                       operating system. The experience so far is really
                       great. It does everything what it should do. I can
                       browse the internet with it, game with it (in the
                       past Google Stadia, now Xbox Cloud), answer my
                       mails and even work on Arch Linux. Even printing
                       worked pretty much out of the box.


                # ⚓ DebugPoint ☛ [Fixed]_VirtualBox_Needs_Microsoft_Visual_C++
                  2019_Redistributable_Package⠀⇛


                       Here’s a quick guide to fix the error “VirtualBox
                       Needs Microsoft Visual C++ 2019 Redistributable
                       Package”.


                       Oracle’s VirtualBox is a popular virtualization
                       software that helps you create guest virtual
                       machines for Linux distributions in any host
                       system.


                # ⚓ The New Stack ☛ Kubernetes_App_Deployment_from_the_Command
                  Line_–_The_New_Stack⠀⇛


                       If you’ve been following my Kubernetes 101 series,
                       you may have discovered that there are ways to make
                       Kubernetes considerably easier. Thanks to MicroK8s
                       and Portainer, the journey doesn’t have to be
                       challenging all the time. But even though you can
                       begin your dive into Kubernetes as a point-and-
                       click affair with Portainer, at some point you
                       might want to be able to work from the command
                       line. That’s not a given but you never know if
                       you’ll be thrown into a situation where you’re
                       asked to deploy an app or service to a Kubernetes
                       cluster and there is no Portainer GUI to be found.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ The_Best_Deck_accessory:_a_Virtual_Monitor?
                  nReal_Air_AR_glasses_Review_–_Boiling_Steam⠀⇛


                       The Steam Deck we all know and love was designed
                       with pragmatism in mind — an all-in-one gaming
                       console that you could use anywhere, uncluttered,
                       unencumbered. It largely succeeded; so much that
                       often the gaming portals and news sites must remind
                       the reader that it is not a gaming PC. It has
                       neither the power nor the peripherals for
                       fulfilling this role, and its 7″ screen while
                       bright and clear is unable to substitute for a big
                       gaming monitor. And while you could attach such
                       monitors to the Deck, they are big, heavy and
                       power-hungry, and definitely not portable.


                       At least, not the physical monitors. How about a
                       virtual monitor? Augmented reality is the merging
                       of the real-world view with a digital image in
                       real-time, done with devices like glasses and
                       headsets. What if the digital image is the monitor,
                       and the augmented reality device are particularly
                       unassuming sunglasses?


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ KDE ☛ KDE_Ships_Frameworks_5.102.0_–_KDE_Community⠀⇛


                             KDE today announces the release of KDE
                             Frameworks 5.102.0.


                             KDE Frameworks are 83 addon libraries to Qt
                             which provide a wide variety of commonly
                             needed functionality in mature, peer reviewed
                             and well tested libraries with friendly
                             licensing terms. For an introduction see the
                             KDE Frameworks release announcement.


                             This release is part of a series of planned
                             monthly releases making improvements
                             available to developers in a quick and
                             predictable manner.


                      # ⚓ 9to5Linux ☛ KDE_Frameworks_5.102_Enables_File
                        Transfers_over_2GB_in_KDE_Connect⠀⇛


                             The KDE Project released today KDE Frameworks
                             5.102 as the latest update to this collection
                             of over 80 add-on libraries to Qt providing
                             commonly needed functionality for the KDE
                             Plasma desktop environment and related apps.


                             KDE Frameworks 5.102 is packed with many
                             changes, but the most prominent ones include
                             support for file transfers over 2GB in size
                             in the KDE Connect app, which lets you
                             transfer files between your mobile device and
                             your computer, but also do other things like
                             receive notifications, control media players,
                             etc.


                      # ⚓ Running_Plasma_on_VisionFive-2_–_cordlandwehr⠀⇛


                             New year, new RISC-V Yocto blog post \o/ When
                             I wrote my last post, I did really not expect
                             my brand new VisionFive-2 board to find its
                             way to me so soon… But well, a week ago it
                             was suddenly there. While unpacking I shortly
                             pondered over my made plans to prepare a
                             Plasma Bigscreen RaspberryPi 4 demo board for
                             this year’s FOSDEM.


                             Obvious conclusion: “Screw it! Let’s do the
                             demo on the VisionFive-2!” — And there we
                             are:


                             After some initial bumpy steps to boot up a
                             first self-compiled U-boot and Kernel (If you
                             unbox a new board, you need to do a
                             bootloader and firmware update first!
                             Otherwise it will not boot the latest
                             VisionFive Kernel) it was surprisingly easy
                             to prepare Yocto to build a core-image-
                             minimal that really boots the whole way up.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ Slashdot ☛ Mabox_Linux_Called_‘Throwback_to_Old-School
                  Linux’_–_Slashdot⠀⇛


                       “If you’ve been itching to try an Arch Linux
                       distribution and want something outside of the
                       usual GNOME/KDE/Xfce desktop environments, Mabox
                       Linux is an outstanding option….” writes ZDNet’s
                       Jack Wallen.


          o § Red Hat⠀➾


                # ⚓ Zooming_Out:_Enterprise-Level_Cloud_Infrastructures [Ed:
                  Red Hat clownwashing]⠀⇛


                # ⚓ Red Hat Official ☛ Building_our_technology_ecosystem:
                  Connecting_a_love_for_learning_to_tech_sales⠀⇛


                       Ana Basso first heard of Red Hat during her time at
                       a technical high school in Brazil, where students
                       had a subject focused on Linux. She clearly
                       remembers their teacher showing them the company’s
                       logo featuring Shadowman and explaining Red Hat’s
                       role in the open source community.


                # ⚓ Red Hat Official ☛ Navigating_5G_transformation:_Key
                  learnings_from_the_Red_Hat_partner_ecosystem⠀⇛


                       In case you missed it, Red Hat recently hosted its
                       annual Open5G event to discuss the latest
                       innovations, challenges and opportunities facing
                       service providers when it comes to 5G networks.
                       Business transformation continues to be top of mind
                       for many in the telecommunications industry as the
                       scope of 5G and the associated cloud infrastructure
                       implications are pushing service providers and
                       operators to rethink the way they deploy and
                       support workloads using open source technologies.


                       At Red Hat, our partner ecosystem is the beating
                       heart behind many of the innovations driving telco
                       business transformation today and into the future,
                       comprising some of the world’s leading service
                       providers, systems integrators, cloud providers and
                       more. During Red Hat’s Open5G event, partners took
                       the virtual stage alongside Red Hat and customers
                       to share their unique experiences and perspectives
                       in 5G. Here are a few key learnings from Red Hat
                       partners:


          o § Devices/Embedded⠀➾


                # ⚓ Market Screener ☛ Digi_International_:_Embedded_Yocto_4.0-
                  r1_LTS_Announcement_|_MarketScreener⠀⇛


                       Digi is delighted to unveil the details of the
                       latest version of Digi Embedded Yocto (DEY) 4.0-r1
                       LTS (Long-term Support). Our customers require a
                       product lifecycle management policy that maintains
                       a stable version of the software for years to avoid
                       compromising the stability or compatibility of
                       applications running on the LTS version. Our
                       renowned and reliable operating system shaped for
                       our feature-rich and secure shielded Digi
                       ConnectCore® system-on-modules (SOM), fully meets
                       these customer needs. Additionally, the
                       enhancements and functionality in this new release
                       will enable the development of robust new device
                       designs for business, industrial, transportation,
                       government, and medical use cases.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_glove_translates_sign_language_using_an
                  array_of_sensors_|_Arduino_Blog⠀⇛


                       For people not familiar with American Sign Language
                       (ASL), being able to recognize what certain hand
                       motions and positions mean is a nearly impossible
                       task. To make this process easier, Hackster.io user
                       ayooluwa98 came up with the idea to integrate
                       various motion, resistive, and touch sensors into a
                       single glove that could convert these signals into
                       understandable text and speech.


                       The system is based around a single Arduino Nano
                       board, which is responsible for taking in sensor
                       data and outputting the phrase that best matches
                       the inputs. The orientation of the hand is
                       ascertained by reading values from the X, Y, and Z
                       axes of a single accelerometer and applying a small
                       change based upon prior calibration. Meanwhile,
                       resistive flex sensors spanning the length of each
                       finger produce a different voltage level according
                       to the bend’s extent.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this
                  week_–_Android_Apps_Weekly⠀⇛


                # ⚓ Make Use Of ☛ 5_Android_Apps_for_Designing_and_Buying_Your
                  Own_Custom_T-Shirts⠀⇛


                # ⚓ 9to5Google ☛ Android_Auto�redesign_rolling_out_draggable
                  seek_bar_in_music_apps⠀⇛


                # ⚓ Notebook Check ☛ Tecno_first-gen_retractable-lens_Android
                  flagship_smartphone_pre-orders_coming_to_Amazon.in_–
                  NotebookCheck.net_News⠀⇛


                # ⚓ CNET ☛ Android_Is_Closing_the_Gap_With_Apple_With_This_New
                  Feature_–_CNET⠀⇛


                # ⚓ Make Use Of ☛ Can_Your_Android_Phone_Be_Tracked_When_It’s
                  Turned_Off?⠀⇛


                # ⚓ Indian Express ☛ The_Google_vs_CCI_slugfest_and_how_it
                  could_impact_Android_users⠀⇛


                # ⚓ Best_Android_Games_Updates_–_Arknights,_Stardew_Valley,_And
                  More_–_Droid_Gamers⠀⇛


                # ⚓ 5_Best_USB-C_Earbuds_with_Microphones_for_Android
                  Smartphones_–_Guiding_Tech⠀⇛


                # ⚓ Android Police ☛ Google_needs_to_raise_the_bar_for_Android
                  updates_again_in_2023⠀⇛


                # ⚓ Dark Reading ☛ Malware_Comes_Standard_With_This_Android_TV
                  Box_on_Amazon⠀⇛


    * § Free, Libre, and Open Source Software⠀➾


          o § GNU Projects⠀➾


                # ⚓ Jérôme_Lejeune_Foundation_adopts_GNU_Health⠀⇛


                       We start 2023 with exciting news for the medical
                       and scientific community!


                       GNU Health has been adopted by he Jérôme Lejeune
                       foundation, a leading organization in the research
                       and management of trisomy 21 (Down Syndrome) and
                       other intellectual disabilities of genetic origin.


                       Lejeune foundation has its headquarters in France,
                       with offices in Argentina, the United States and
                       Spain.


                # ⚓ GNU ☛ GNU_Binutils_2.40_released⠀⇛


                       Hi Everyone,


                       We are pleased to announce that version 2.40 of the
                       GNU Binutils project
                       sources have been released and are now available
                       for download at:


                       https://ftp.gnu.org/gnu/binutils


                       https://sourceware.org/pub/binutils/releases/


                # ⚓ Sean_Whitton:_Always_running_Emacs_under_gdb⠀⇛


                       The emacsclient(1) program is used to connect to
                       Emacs running as a daemon. emacsclient(1) can go in
                       your EDITOR/VISUAL environment variables so that
                       you can edit things like Git commit messages and
                       sudoers files in your existing Emacs session,
                       rather than starting up a new instances of Emacs.
                       It’s not only that this is usually faster, but also
                       that it means you have all your session state
                       available – for example, you can yank text from
                       other files you were editing into the file you’re
                       now editing.


                       Another, somewhat different use of emacsclient(1)
                       is to open new Emacs frames for arbitrary work, not
                       just editing a single, given file. This can be in a
                       terminal or under a graphical display manager. I
                       use this as often as I invoke emacsclient(1) via
                       EDITOR/VISUAL. I use emacsclient -nc to open new
                       graphical frames and emacsclient -t to open new
                       text-mode frames, the latter when SSHing into my
                       work machine from home, or similar. In each case,
                       all my buffers, command history etc. are available.
                       It’s a real productivity boost.


                       Some people use systemd socket activation to start
                       up the Emacs daemon. That way, they only need ever
                       invoke emacsclient, without any special options,
                       and the daemon will be started if not already
                       running. In my case, emacsclient on PATH is a
                       wrapper script that checks whether a daemon is
                       running and starts one if necessary. The main
                       reason I have this script is that I regularly use
                       both the installed version of Emacs and in-tree
                       builds of Emacs out of emacs.git, and the script
                       knows how to choose what to launch and what to try
                       to connect to. In particular, it ensures that the
                       in-tree emacsclient(1) is not used to try to
                       connect to the installed Emacs, which might fail
                       due to protocol changes. And it won’t use the in-
                       tree Emacs executable if I’m currently recompiling
                       Emacs.


          o § Programming/Development⠀➾


                # ⚓ Software_testing,_and_why_I’m_unhappy_about_it⠀⇛


                       Automated testing of software is great.
                       Unfortunately, what’s commonly considered best
                       practice for how to integrate testing into the
                       development flow is a bad fit for a lot of
                       software. You know what I mean: You submit a pull
                       request, some automated testing process is kicked
                       off in the background, and some time later you get
                       back a result that’s either Green (all tests
                       passed) or Red (at least one test failed). Don’t
                       submit the PR if the tests are red. Sounds good,
                       doesn’t quite work.


                       There is Software Under Test (SUT), the software
                       whose development is the goal of what you’re doing,
                       and there’s the Test Bench (TB): the tests
                       themselves, but also additional relevant parts of
                       the environment like perhaps some hardware device
                       that the SUT is run against.


                       The above development practice works well when the
                       SUT and TB are both defined by the same code
                       repository and are developed together. And
                       admittedly, that is the case for a lot of useful
                       software. But it just so happens that I mostly tend
                       to work on software where the SUT and TB are
                       inherently split. Graphics drivers and shader
                       compilers implement some spec (like Vulkan or
                       Direct3D), and an important part of the TB are a
                       conformance test suite and other tests, the bulk of
                       which are developed separately from the driver
                       itself. Not to mention the GPU itself and other
                       software like the kernel mode driver. The point is,
                       TB development is split from the SUT development
                       and it is infeasible to make changes to them in
                       lockstep.


                # ⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RApiDatetime_0.0.8
                  on_CRAN:_Maintenance⠀⇛


                       RApiDatetime provides a number of entry points for
                       C-level functions of the R API for Date and
                       Datetime calculations. The functions asPOSIXlt and
                       asPOSIXct convert between long and compact datetime
                       representation, formatPOSIXlt and Rstrptime convert
                       to and from character strings, and POSIXlt2D and
                       D2POSIXlt convert between Date and POSIXlt
                       datetime. Lastly, asDatePOSIXct converts to a date
                       type. All these functions are rather useful, but
                       were not previously exported by R for C-level use
                       by other packages. Which this package aims to
                       change.


                # ⚓ Barry Kauler ☛ gui_engine_runs_in_initrd⠀⇛


                       I posted yesterday about compiling ‘dialog’
                       statically, enabling text-mode GUIs in the initrd:


                       https://bkhome.org/news/202301/first-bootup-2-
                       letter-language-asked-in-initrd.html


                       ‘dialog’ is completely stand-alone, doesn’t require
                       any shared libraries, and is 508KB. It supports
                       unicode characters.


                       All of the utilities in the initrd are statically-
                       linked; ‘busybox’ is another example.


                       [...]


                       The example is named ‘example’ and is 304KB. That
                       is a statically-link standalone application. Most
                       of the size is the linked-in libsdl, so adding more
                       features to the app won’t increase the size much.


                       Very limited widgets, no documentation, but very
                       simple and small C code. So definitely interested
                       in taking it on as a project. Might be of interest
                       to someone else also. First task — there is no way
                       to exit from the example, had to do a hard power-
                       off.


                # ⚓ What_is_ActiveRecord_becomes_from_Rails⠀⇛


                       Have you heard about the ActiveRecord becomes
                       method from Rails? Maybe it’ll come handy one day.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ How_to_prevent_an_infinite_loop⠀⇛


    * § Leftovers⠀➾


          o ⚓ Tedium ☛ So_Many_Itches_To_Scratch⠀⇛


                 It may be weird to consider in a world where we have so
                 many ways to interact with things through touch, but we
                 don’t use all of those types of interaction to
                 communicate with a computer. To offer an example:
                 Scratching. Often done with fingernails, quarters, or
                 other somewhat abrasive materials, it’s a common type of
                 gesture that has no true equivalent in the world of smart
                 devices (well, unless you scratch your screen). I’ve been
                 thinking a lot about the nature of scratching recently,
                 and for today’s Tedium, I wanted to offer up every single
                 scrap of thinking on scratching. I’m feelin’ kinda itchy.


                 [...]


                 Thanks to its use of a latex-based ink or varnish that
                 covers up the winning details until you scratch them off,
                 scratch-offs are naturally multi-layered, and that
                 general design allows for things to be hidden. In some
                 ways, the coating is the key element—but in others, it’s
                 the underlying algorithms behind the game of chance.
                 Maybe it’s the combination of the two.


                 As the Detroit Free Press reported late last year, the
                 invention comes to us from an early computer scientist
                 named John Koza, one of the first graduates of the
                 University of Michigan’s computer science program. Koza’s
                 innovation was not the scratch-off material itself—which
                 was already in wide use by his employer in undergrad at
                 the time, the sweepstakes company J&H International—but
                 the addition of algorithms that helped turned lottery
                 games into things that could be played—and won—instantly,
                 rather than things that came with a long wait.


          o § Science⠀➾


                # ⚓ Omicron Limited ☛ James_Webb_telescope_reveals_Milky
                  Way–like_galaxies_in_young_universe⠀⇛


                       New images from NASA’s James Webb Space Telescope
                       (JWST) reveal for the first time galaxies with
                       stellar bars—elongated features of stars stretching
                       from the centers of galaxies into their outer
                       disks—at a time when the universe was a mere 25% of
                       its present age. The finding of so-called barred
                       galaxies, similar to our Milky Way, this early in
                       the universe will require astrophysicists to refine
                       their theories of galaxy evolution.


                       Prior to JWST, images from the Hubble Space
                       Telescope had never detected bars at such young
                       epochs. In a Hubble image, one galaxy, EGS-23205,
                       is little more than a disk-shaped smudge, but in
                       the corresponding JWST image taken this past
                       summer, it’s a beautiful spiral galaxy with a clear
                       stellar bar.


                # ⚓ BoingBoing ☛ 1940s_Bell_Telephone_introduces_the_mobile
                  phone_|_Boing_Boing⠀⇛


                       This video is fun. I miss the ring of an old Bell
                       telephone. I have one here in the house but no
                       landline to plug it into, and so it sits on my
                       desk. I also have a candlestick phone that is
                       nothing more than art.


          o § Security⠀➾


                # ⚓ CyberRisk Alliance LLC ☛ Sigstore_announces_the_first
                  stable_release_of_code_and_certificate_signing_tool_for
                  Python [Ed: Centralisation of "trust" (for software in this
                  case) brings a whole host of new issues]⠀⇛


                       Sigstore community today announced the first stable
                       release of sigstore-python, improving software
                       supply chain security and paving the way for other
                       client implementations of Sigstore that are in
                       earlier stages.


                       Sigstore is an open source project launched by
                       Linux Foundation with the goal of providing free
                       and stable services for all developers to easily
                       sign, verify and protect their software projects.
                       While code signing is a valuable tool to prevent
                       hackers from co-opting patching systems and
                       delivering malware, it is difficult to implement in
                       open source projects given the complexity of key
                       management.


                # ⚓ CyberRisk Alliance LLC ☛ Security_researchers_report_Linux
                  malware_with_cryptocurrency_miner_payload [Ed: The problem
                  here is weak passwords, not "Linux" or "SSH"]⠀⇛


                       “It is presumed that after successful
                       authentication through a dictionary attack on
                       inadequately managed Linux SSH servers, various
                       malware were installed on the target system. This
                       bot supports not only DDoS attacks such as TCP
                       flood, UDP flood, and HTTP flood, but various other
                       features including command execution, reverse
                       shell, port scanning, and log deletion,”
                       researchers said.


                # ⚓ Slashdot ☛ New_Linux_Malware_Downloader_for_Compromised
                  Servers_Spotted_in_the_Wild [Ed: Slashdot helps Microsoft
                  sites stagmatise "Linux" as not secure; but the problem here
                  is weak passwords, not Linux; This headline is intentionally
                  misleading, just like the Microsofters']⠀⇛


                # ⚓ TechRadar ☛ This_new_Linux_malware_floods_machines_with
                  cryptominers_and_DDoS_bots [Ed: So weak passwords are the
                  fault of Linux now?]⠀⇛


                # ⚓ Red Hat Official ☛ A_Brief_History_of_Cryptography⠀⇛


                       Cryptology is a young science.


                       Though it has been used for thousands of years to
                       hide secret messages, systematic study of
                       cryptology as a science (and perhaps an art) just
                       started around one hundred years ago.


                       The first known evidence of the use of cryptography
                       (in some form) was found in an inscription carved
                       around 1900 BC, in the main chamber of the tomb of
                       the nobleman Khnumhotep II, in Egypt. The scribe
                       used some unusual hieroglyphic symbols here and
                       there in place of more ordinary ones. The purpose
                       was not to hide the message but perhaps to change
                       its form in a way which would make it appear
                       dignified. Though the inscription was not a form of
                       secret writing, but incorporated some sort of
                       transformation of the original text, and is the
                       oldest known text to do so. Evidence of some use of
                       cryptography has been seen in most major early
                       civilizations. “Arthshashtra”, a classic work on
                       statecraft written by Kautalya, describes the
                       espionage service in India and mentions giving
                       assignments to spies in “secret writing” – sounds
                       like an ancient version of James Bond?


                       Fast forwarding to around 100 BC, Julius Caesar was
                       known to use a form of encryption to convey secret
                       messages to his army generals posted in the war
                       front. This substitution cipher, known as Caesar
                       cipher, is perhaps the most mentioned historic
                       cipher in academic literature. (A cipher is an
                       algorithm used for encryption or decryption.) In a
                       substitution cipher, each character of the plain
                       text (plain text is the message which has to be
                       encrypted) is substituted by another character to
                       form the cipher text (cipher text is the encrypted
                       message). The variant used by Caesar was a shift by
                       3 cipher. Each character was shifted by 3 places,
                       so the character ‘A’ was replaced by ‘D’, ‘B’ was
                       replaced by ‘E’, and so on. The characters would
                       wrap around at the end, so ‘X’ would be replaced by
                       ‘A’.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Bocchi_the_Rock!_/_ぼっち・ざ・ろっく!⠀⇛


                       Readers of my gemlog may have guessed that I quite
                       like music-themed anime, so how could I have missed
                       out on Bochi the Rock. It started out as probably
                       the most invisible show of the season, but wao,
                       that surely changed quickly.


                # ⚓ Moving_to_Hugo⠀⇛


                       I started this website around 2008 at
                       wordpress.com. Later in 2012[1], I moved to Jekyll
                       and started blogging on Markdown. I started using
                       git to manage the code and host the website first
                       on GitHub Pages and later on Netlify. Since then,
                       I’ve slowly moved other projects from Jekyll to
                       Hugo. I still have a few in the good old ruby tech,
                       the biggest one, without any doubt, being the daily
                       geospatial digest[2].


                # ⚓ Email_training⠀⇛


                       By the end of last year, I enrolled in
                       cibervoluntarios[1], an NGO that provides free
                       training about Information technologies to seniors
                       and young people, and other groups with exclusion
                       risk. It’s an entirely virtual organization where
                       volunteers sign up for proposed activities, and the
                       organization provides all the materials and
                       guidance. Then on the training day, you show up and
                       do the gig.


                # ⚓ [Corrected URL] 🔤SpellBinding:_AEHIRYW_Wordo:_AMITY⠀⇛


          o § Technical⠀➾


                # ⚓ Allotment_Plan:_2023⠀⇛


                       This year, I’m going to do some high-intensity
                       growing on the allotment, following a pretty
                       relaxed quarter-year in 2022 where I just cut back
                       overgrowth and harvested things put in by the
                       previous owner.


                # ⚓ Adding_a_minimal_fingerd_to_bubblewrapped_services_(bws)⠀⇛


                       Some time back Toby Kurien published details and
                       code about his favourite setup regarding self
                       hosting services at home. He did put in quite some
                       effort to make this simple to install and run. I
                       quite like this setup and I have written a minimal
                       finger daemon to run in this setup.


                # ⚓ Perception_of_what_the_Internet_looks_like_today⠀⇛


                       I came across DOStodon, a Mastodon client for MS-
                       DOS. I looked at screenshots and I saw today’s
                       Internet distorted by the crystal of time. So there
                       is almost everything in its place, but it looks
                       different. A similar feeling accompanies browsing a
                       world map in MapSCII, and probably during the usage
                       of other niche tools.


                       So we have a vision of today’s Internet in our
                       mind. It could be similar to the vision of the
                       black-and-white film era, which made our minds feel
                       that people, cities, and their activities then were
                       less colorful than now. Or characteristic colors of
                       Kodachrome film, which is emulated today by
                       software color palettes.


                # § Internet/Gemini⠀➾


                      # ⚓ Tidying_up_gemini.circumlunar.space_user_capsules⠀⇛


                             In earlier times, I offered free sftp-based
                             Geminispace at this server, and sixty or so
                             people took advantage before I discontinued
                             the offer. Some of those capsules continue to
                             be regularly updated to this day, which makes
                             me very happy. Others have been abandoned,
                             which is to be expected, but some never even
                             got off the ground in the first place. I’d
                             like to start tidying the place up a bit.


                # § Programming⠀➾


                      # ⚓ A_Wafer_Thin_Common_LISP_Package_Primer⠀⇛


                             Common LISP packages tend to trip up noobs
                             presumably only familiar with packages as
                             found in other languages; in those languages
                             you usually have a file that contains a
                             package and that package is only defined in
                             that one file. We might call this a file-
                             package. This is obviously a simplification;
                             usually other languages have various ways to
                             break the file-package rule, e.g. code to
                             import things into or from somewhere else,
                             dynamic loading, monkey patching, LD_PRELOAD,
                             and worse.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
World Wide Web but a lot lighter.


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